1

Numerical differentiation formulas for a function f are typically found by doing which of the following?

Choose one answer.

A. Finding a zero of f' | ||

B. Approximating f by a polynomial P and differentiating P | ||

C. Differentiating a Fourier transform of f and then applying an inverse transform | ||

D. Finding the slope of f at two randomly generated points | ||

E. None of the above |

Question
2

Let . Approximate using the 2-point difference formula with .

Choose one answer.

A. 2.0 | ||

B. 2.1 | ||

C. 1.9 | ||

D. 0.21 | ||

E. 0.19 |

Question
3

For fixed , , and finite difference formula, there is an that minimizes the error in the computed approximation to . Why?

Choose one answer.

A. Every difference formula has a truncation error formula that can be minimized. | ||

B. High degree interpolating polynomials oscillate too much. | ||

C. Underflows increase as . | ||

D. Overflows increase as . | ||

E. Rounding errors increase as . |

Question
4

Use a 3-point centered difference formula with to
approximate , where

. Identify the best 4 significant digit approximate below.

. Identify the best 4 significant digit approximate below.

Choose one answer.

A. 2.000 | ||

B. 1.999 | ||

C. 1.989 | ||

D. 1.899 |

Question
5

If f(x) is only known at the uniformly spaced grid points and a approximation to is desired at each , then what combination of differentiation rules could be used?

Choose one answer.

A. Centered difference formula at each | ||

B. 3-point difference formulas, forward difference at left endpoint, backward difference at right endpoint, and centered difference elsewhere | ||

C. Backward difference on left half of gridpoints, and forward difference on right half | ||

D. Alternating forward and backward differences, beginning with backward difference at |

Question
6

What is the truncation error term for the 3-point centered difference formula for approximating ?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
7

Let . Approximate using the 2-point difference formula with .

Choose one answer.

A. 2.0 | ||

B. 2.1 | ||

C. 1.9 | ||

D. 0.21 | ||

E. 0.19 |

Question
8

Which of the following statements about composite Newton-Cotes quadrature rules is true?

Choose one answer.

A. They use a Taylor polynomial for f'. | ||

B. They integrate a piecewise polynomial approximation to f. | ||

C. They are a type of Monte Carlo method. | ||

D. They require orthogonal polynomial integration. | ||

E. None of the above |

Question
9

Use Simpson's method () to approximate . Choose the best 4 significant digit answer below.

Choose one answer.

A. 0.3750 | ||

B. 0.5000 | ||

C. 0.6667 | ||

D. 0.3333 | ||

E. 0.2500 |

Question
10

Use composite trapezoidal rule with to approximate
. Choose the best 4 significant digit answer below.

Choose one answer.

A. 0.3750 | ||

B. 0.5000 | ||

C. 0.3333 | ||

D. 1.500 | ||

E. 0.3125 |

Question
11

How is the adaptive quadrature method adaptive?

Choose one answer.

A. Subdivides if the integral is too large. | ||

B. It subdivides if the derivative is too large. | ||

C. It subdivides if rounding error exceedes truncation error. | ||

D. It subdivides if error estimate is too large. |

Question
12

Newton-Cotes quadrature rules for a function f are typically found by doing which of the following?

Choose one answer.

A. Using a left sided Riemann sum | ||

B. Approximating f by a polynomial P and integrating P | ||

C. Integrating a Fourier transform of f and then applying an inverse transform | ||

D. Finding the average height of f at n randomly generated points | ||

E. None of the above |

Question
13

In a floating point system with 3 decimal digits in the fractional part, what is the result of 7.234 + 5.784?

Choose one answer.

A. 13.02 | ||

B. 13.01 | ||

C. 13.0 | ||

D. 13.1 | ||

E. None of the above |

Question
14

What is the relative error in the 3 decimal digit floating point arithmetic computation (123 + 0.449)-122?

Choose one answer.

A. 31% | ||

B. 0.449 | ||

C. 44.9% | ||

D. 0 | ||

E. 1.449 |

Question
15

What value results in the 3 decimal digit floating point arithmetic computation (123.3 + 0.4)-122.7?

Choose one answer.

A. 1 | ||

B. 0.4 | ||

C. 0 | ||

D. 0 | ||

E. 1.3 |

Question
16

In a floating point system with t digits in the fractional part, if x and y share the same normalized exponent and the same g fractional digits, then how
many digits of fl(x-y) are known to be correct?

Choose one answer.

A. t-g | ||

B. g | ||

C. All t | ||

D. 0 | ||

E. It depends on the compiler. |

Question
17

In general, which of the following holds for the floating point addition of two or three floating point numbers whose sum does not overflow or underflow?

Choose one answer.

A. Both commutative and associative | ||

B. Commutative but not associative | ||

C. Neither commutative nor associative | ||

D. Associative but not commutative |

Question
18

Swamping and cancellation both describe a loss of information. Select the statement below that best describes their effects.

Choose one answer.

A. Swamping does not violate the fundamental axiom of floating point arithmetic, but cancellation does. | ||

B. Cancellation loses precision, while swamping does not. | ||

C. Swamping loses precision, while cancellation does not. | ||

D. Swamping can only happen with multiplication and cancellation only with addition. |

Question
19

The machine epsilon is nearest to which of the following?

Choose one answer.

A. Underflow | ||

B. Overflow | ||

C. The distance between 1 and the nearest float to 1 | ||

D. 1/Overflow |

Question
20

Suppose x and y are floats and fl(x+y)=fl(x). What can be said of y?

Choose one answer.

A. y underflowed. | ||

B. y=0. | ||

C. |y| is less than |x|*(machine epsilon). | ||

D. fl(0+y)=0. |

Question
21

With a fixed length floating point word, adding a bit to the fractional part requires removing a bit from the exponent. Which of the following statements
describes how this affects the set of floats?

Choose one answer.

A. The floats are farther apart but have a larger range. | ||

B. The floats are nearer each other but have a smaller range. | ||

C. There are more floats. | ||

D. Underflow is smaller. | ||

E. The machine precision grows. |

Question
22

Suppose a floating point system can represent K floats. If one bit is added to that floating point word, about how many floats can then be represented?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. | ||

E. |

Question
23

What can be said of any solution, x, to fl(1+x)=1?

Choose one answer.

A. . | ||

B. . | ||

C. . | ||

D. . |

Question
24

Fill in the blank. If it can be shown that the result of a computation is the exact answer to a nearby problem, then we say the computation is
____________.

Choose one answer.

A. Highly accurate | ||

B. Rounding correct | ||

C. Backward stable | ||

D. Well conditioned | ||

E. Robust |

Question
25

If x + y is smaller than both x and y, information in the sum x + y is lost. What is this called?

Choose one answer.

A. Swamping | ||

B. Machine epsilon | ||

C. Truncation error | ||

D. Cancellation | ||

E. None of the above |

Question
26

Fill in the blank. If a small change to a problem leads to a large change in its solution, then we say that the problem is ______________.

Choose one answer.

A. Backward stable | ||

B. Well conditioned | ||

C. Robust | ||

D. Ill conditioned | ||

E. Highly accurate |

Question
27

Problem has input and output . A small perturbation gives a new input and a new output . A relative condition number for problem should satisfy which of the following?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
28

Problem has input and output . A small perturbation gives a new input and a new output . An absolute condition number for problem should satisfy which of the following?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
29

Under what conditions on a problem and method are we guaranteed a good solution?

Choose one answer.

A. Problem is stable and method is backward stable. | ||

B. Problem is stable and method is well conditioned. | ||

C. Problem is well conditioned and method is well conditioned. | ||

D. Problem is well conditioned and method is backward stable. |

Question
30

What is an upper bound on the relative error between two neighboring floats called?

Choose one answer.

A. Cancellation limit | ||

B. Machine epsilon | ||

C. Underflow | ||

D. Backward error | ||

E. None of the above |

Question
31

In a floating point system with 3 decimal digits in the fractional part, what floating point number would be used to represent 0.0032419?

Choose one answer.

A. 0.003 | ||

B. 0.00324 | ||

C. 0.003242 | ||

D. 0.00 | ||

E. None of the above |

Question
32

In a floating point system with 3 decimal digits in the fractional part, what floating point number would be used to represent 142.32419?

Choose one answer.

A. 142 | ||

B. 142.324 | ||

C. 142.3 | ||

D. 142.32 | ||

E. None of the above |

Question
33

When a large magnitude and small magnitude float are added, information from the smaller number is lost. What is this called?

Choose one answer.

A. Chopping | ||

B. Cancellation | ||

C. Truncation Error | ||

D. Swamping | ||

E. Tail Error |

Question
34

The term Initial Value Problem is best defined in this course as which of the following?

Choose one answer.

A. , where with initial value | ||

B. | ||

C. Given , find . | ||

D. Find such that . | ||

E. |

Question
35

Which of the following is an initial value problem?

Choose one answer.

A. . | ||

B. . | ||

C. . | ||

D. . |

Question
36

A shooting method for a boundary value problem requires what 2 numerical methods?

Choose one answer.

A. An interpolator and a numerical differentiation rule | ||

B. A quadrature rule and an IVP solver | ||

C. A root finder and a quadrature rule | ||

D. An IVP solver and a root finder |

Question
37

What is the Euler slope?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. | ||

E. None of the above |

Question
38

In theory, the error in Euler's method can be made arbitrarily small by varying h, why is this not the case in practice?

Choose one answer.

A. Because of rounding errors | ||

B. Because of truncation errors | ||

C. As , the truncation errors explode. | ||

D. As , the truncation errors explode. |

Question
39

When converting a scalar differential equation of order n into a system of first order differential equations, how many dimensions are needed to represent
the solution vector?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. | ||

E. None of the above |

Question
40

Why does an explicit 3-step method for IVP require the use of a single-step method?

Choose one answer.

A. Because it averages 3 values in | ||

B. Because Euler's method is unstable | ||

C. Because the corrector needs a prediction | ||

D. Because a 3-step method needs 2 previous approximations to y | ||

E. Because a 3-step method needs 3 previous approximations to y |

Question
41

An explicit 3 step method needs to use a single step method, but Euler's method is a bad choice. Why shouldn't one use Euler's method in this setting?

Choose one answer.

A. Euler's method is unstable. | ||

B. Eulers method has local truncation error , which is lower than a 3 step method. | ||

C. Euler's method has large rounding errors. | ||

D. Euler's method is too slow for a 3 step method. | ||

E. Taylor methods are more general. |

Question
42

In a multistep predictor-corrector method, what type of method is the corrector?

Choose one answer.

A. The corrector is typically a higher order Runge Kutta method. | ||

B. The corrector is typically a low order Runge Kutta method. | ||

C. The corrector is typically an implicit method. | ||

D. The corrector is typically a higher order explicit multistep method. |

Question
43

The Adams-Bashforth 2-step (AB2) method has the iteration . Consider the IVP . Select the best 4
significant digit approximation below to the AB2 value for , taking i, and .

Choose one answer.

A. 1.297 | ||

B. 1.015 | ||

C. 0.7650 | ||

D. 1.547 |

Question
44

How many function evaluations are required per timestep for an Adams-Bashforth method of order ?

Choose one answer.

A. 1 | ||

B. 2 | ||

C. 4 | ||

D. 5 | ||

E. 6 |

Question
45

Which of the following is an implicit method?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
46

Which of the following is a general purpose single step method?

Choose one answer.

A. Taylor's method | ||

B. Adams-Bashforth's method | ||

C. Adams-Moulton's method | ||

D. Runge-Kutta's method |

Question
47

Consider the IVP . Approximate using Euler's method with . Select the best 3 significant digit answer below.

Choose one answer.

A. 3.00 | ||

B. 3.75 | ||

C. 2.00 | ||

D. 4.55 | ||

E. 6.30 |

Question
48

Variable step-size methods all require which of the following?

Choose one answer.

A. A good starting guess | ||

B. An error estimate | ||

C. Multistep method | ||

D. A list of allowable step sizes |

Question
49

Choose the iteration below which represents the Runge-Kutta method called the midpoint method.

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
50

Choose the iteration below which represents the Runge-Kutta method called the modified Euler or Heun's method.

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
51

How many function evaluations are required per timestep for a Runge-Kutta method of order ?

Choose one answer.

A. 1 | ||

B. 2 | ||

C. 4 | ||

D. 5 | ||

E. 6 |

Question
52

How many function evaluations are required per timestep for a Runge-Kutta method of order ?

Choose one answer.

A. 1 | ||

B. 2 | ||

C. 4 | ||

D. 5 | ||

E. 6 |

Question
53

Consider the IVP . Which of the following
iterations correspond to the Taylor method of order 2 for this IVP?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
54

If an IVP is stiff, what restriction is imposed on the solver?

Choose one answer.

A. Stiff IVP's require a small timestep. | ||

B. Stiff IVP's require predictor-corrector methods. | ||

C. Stiff IVP's require Taylor methods. | ||

D. Stiff IVP's require high order methods. |

Question
55

What qualitative property should a method have when applied to the test problem ?

Choose one answer.

A. . | ||

B. bounded for all . | ||

C. bounded for all . | ||

D. . |

Question
56

Why are Taylor methods not as general purpose as Runge-Kutta methods?

Choose one answer.

A. Taylor methods require the evaluation of for $k>1$. | ||

B. Taylor polynomials oscilate too much. | ||

C. Taylor methods replace derivatives with function evaluations. | ||

D. Taylor methods are not parallelizable because of nested function evaluations. |

Question
57

Fill in the blank. Ignoring rounding errors, a successful IVP method with local truncation error of order k should have global error of order ________.

Choose one answer.

A. k+1 | ||

B. k/2 | ||

C. 2k | ||

D. k-1 |

Question
58

All single step IVP methods have a common iteration . If , what is the value of that would guarantee was on the solution curve?

Choose one answer.

A. . | ||

B. . | ||

C. . | ||

D. . |

Question
59

What conditions on an initial value problem guarantee a unique solution?

Choose one answer.

A. is smooth enough for all . | ||

B. is continuous in . | ||

C. is nonsingular. | ||

D. The initial is close enough to the solution. | ||

E. has a fixed point such that . |

Question
60

Fill in the blank. A second order ordinary differential equation, requires two extra conditions for uniqueness of solution. If these conditions are and , then the differential equation is called a(n) ___________.

Choose one answer.

A. Partial differential equation | ||

B. Ill posed differential equation | ||

C. Side-condition differential equation | ||

D. Boundary value problem |

Question
61

Which of the following gives sufficient conditions for to have a unique solution?

Choose one answer.

A. . | ||

B. continuous in , and exists in . | ||

C. continuous in , and continuous at . | ||

D. well-defined at the critical point . |

Question
62

The Weierstrauss approximation theorem says that under certain conditions on and for any , there is a polynomial , such that for all . Choose from below the weakest such conditions on ?

Choose one answer.

A. has a power series representation on . | ||

B. is continuous on . | ||

C. has one continuous derivative on . | ||

D. has no poles on . |

Question
63

Which of the following is true for ?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
64

Which of the following is true for ?

Choose one answer.

A. for near . | ||

B. for near . | ||

C. for near . | ||

D. for near . |

Question
65

What is the minimum number of multiplications required to evaluate for arbitrary real ?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
66

When dividing a polynomial of degree by the polynomial , the remainder will be a scalar. What choice below best describes this
scalar?

Choose one answer.

A. It has degree or degree . | ||

B. It is . | ||

C. It is . | ||

D. It is a root of . | ||

E. It is deflated. |

Question
67

Let be a zero of a polynomial of degree n > 10, and suppose we have an initial approximation
such that both Newton's method and the secant
method both converge, and an interval of length
about containing and for which bisection will converge to . For this specialized case, list from fastest to slowest, the three
methods.

Choose one answer.

A. Newton's, secant, bisection | ||

B. Newton's, bisection, secant | ||

C. Secant, Newton's, bisection | ||

D. Secant, bisection, Newton's | ||

E. Bisection, Newton's, secant |

Question
68

Fill in the blank. If is a root of a polynomial
of degree , then is a polynomial of degree . Finding the remaining roots of by finding the roots of is called ______________.

Choose one answer.

A. The Chinese remainder method | ||

B. Degree slashing | ||

C. Synthetic division | ||

D. Deflation |

Question
69

Why don't we use the quintic equation to find the zeros of a polynomial of degree 5 or less?

Choose one answer.

A. Newton's method is more accurate. | ||

B. Extracting roots is very slow on a computer. | ||

C. It is pretend. | ||

D. Rounding errors and truncation errors work against each other. |

Question
70

A Hermite interpolator is constructed for values and slopes at 4 knots. What can be said about the degree of this interpolator?

Choose one answer.

A. Its degree is 4. | ||

B. Its degree is no more than 4. | ||

C. Its degree is no more than 7. | ||

D. Its degree must be more than 7. | ||

E. None of the above |

Question
71

What type of polynomial interpolator would be appropriate for the data ?

Choose one answer.

A. Hermite | ||

B. Taylor | ||

C. Lagrange | ||

D. Piecewise linear | ||

E. Quadratic spline |

Question
72

If is the Lagrange interpolator for the knots
and , what is ?

Choose one answer.

A. 2.6 | ||

B. 2.8 | ||

C. 3.9 | ||

D. 1.5 | ||

E. 2.9 |

Question
73

Suppose we approximate over using the Lagrange interpolator for the nodes and . Use the Lagrange error term (remainder) to get an upper bound on the
error.

Choose one answer.

A. | ||

B. | ||

C. | ||

D. | ||

E. There is no error; it is well posed. |

Question
74

How many polynomials exist which interpolate the data where for ?

Choose one answer.

A. Only one | ||

B. Depends upon the knot positions | ||

C. n+1 Lagrange basis functions | ||

D. Infinitely many |

Question
75

Suppose is the Lagrange interpolator for the knots
with for . If is a polynomial of degree satisfying , for . What can be said of ?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. is a Hermite interpolator. | ||

E. None of the above |

Question
76

If is the Lagrange interpolator for the knots
and , what is ?

Choose one answer.

A. 4.1 | ||

B. 3.8 | ||

C. 3.9 | ||

D. 3.5 | ||

E. 2.9 |

Question
77

A Taylor polynomial is a special case of what type of interpolator?

Choose one answer.

A. Osculating polynomial | ||

B. Lagrange interpolator | ||

C. Hermite interpolator | ||

D. Vandermonde interpolator | ||

E. None of the above |

Question
78

Consider the Lagrange basis functions for the knots , and . How many basis functions are there
for this set of knots, and what are their degrees?

Choose one answer.

A. Three basis functions, each of degree 2 | ||

B. Two basis functions, each of degree two | ||

C. Two basis functions, each of degree three | ||

D. Three basis functions, of degree 1, degree 2 and degree 3 |

Question
79

Let be the value of the derivative of a curve at the point . Suppose we want to interpolate the data and . If a Vandermonde matrix is constructed for the interpolating
polynomial, what is its size?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
80

Let be the value of the derivative of a curve at the point . Suppose we want to interpolate the data and . In general, what is the degree of such an interpolating
polynomial?

Choose one answer.

A. 4 | ||

B. 5 | ||

C. 6 | ||

D. 7 |

Question
81

If is smooth enough in a neighborhood of
, then the Taylor polynomial of degree n for
at approximates with error_________.

Choose one answer.

A. | ||

B. | ||

C. | ||

D. | ||

E. None of the above |

Question
82

What is the Taylor polynomial of degree 1 for at
?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. | ||

E. |

Question
83

What is the Taylor polynomial of degree 1 for at
?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. | ||

E. |

Question
84

The linear Taylor polynomial at for is . Use this Taylor polynomial to approximate . Select the best 5 significant digit answer to the Taylor approximation.

Choose one answer.

A. 10.149 | ||

B. 10.150 | ||

C. 5.5074 | ||

D. 9.8500 | ||

E. 10.001 |

Question
85

The set of polynomials of degree n over a field is a vector space of which dimension?

Choose one answer.

A. n | ||

B. 2n | ||

C. n+2 | ||

D. n/2 | ||

E. None of the above |

Question
86

The method of bisection can find a zero of a continuous function, if which of the following is true of the initial data?

Choose one answer.

A. It is close to the correct answer. | ||

B. It gives the bisector of the zero. | ||

C. It is not complex. | ||

D. It gives function height and slope. | ||

E. None of the above |

Question
87

Bisection is used on an initial interval [a,b], where b-a=2. How many iterations are required for the current interval to have length 1/16?

Choose one answer.

A. 4 | ||

B. 5 | ||

C. 6 | ||

D. 8 | ||

E. 10 |

Question
88

If the method of bisection is used to find a zero of a continuous function f(x), and an initial interval [a,b] is given such that f(a)f(b) < 0, counting
multiplicity, what can be said about the zeros of f in [a,b]?

Choose one answer.

A. f has exactly one zero in [a,b]. | ||

B. f has 0, 1, or infinitely many zeros in [a,b]. | ||

C. f has an even number of zeros in [a,b]. | ||

D. f has an odd number of zeros in [a,b]. |

Question
89

Which method cannot be used to find a root of ?

Choose one answer.

A. Newton's method | ||

B. Bisection method | ||

C. Secant method | ||

D. Meuller's method | ||

E. False position |

Question
90

Suppose it is known that the continuous function
has exactly 1 root strictly between 0 and 1, and it is not a double root. Which method can guarantee an approximate root with error less than 0.0001 in
fewer than 14 function evaluations?

Choose one answer.

A. Newton's method | ||

B. Secant method | ||

C. Bisection method | ||

D. None of the above |

Question
91

Suppose it is known that the continuous function
has exactly 1 root strictly between 0 and 1, and it is a double root. An encrypted subroutine will return given any . Which of the following methods cannot be applied to this problem?

Choose one answer.

A. Neither Newton's nor bisection can be applied here. | ||

B. Neither Newton's nor secant can be applied here. | ||

C. Bisection cannot be applied here. | ||

D. Newton's method cannot be applied here. |

Question
92

Which of the following gives a rough estimate of convergence for bisection and Newton's method (in the case each converge at their respective order of
convergence)?

Choose one answer.

A. For each iteration, Newton's method adds 1 correct bit and bisection add about 0.5 correct bits. | ||

B. For each of the two iterations, Newton's method doubles number of correct bits and bisection adds 2 correct bits. | ||

C. For each iteration, Newton's method doubles the number of correct bits and bisection adds 1 correct bit. | ||

D. For each iteration, Newton's method adds two correct bits and bisection adds 1 correct bit. |

Question
93

Suppose Newton's method begins with an initial approximation, x_{0}._{ }The next approximation, x_{1}, is found by doing which of
the following?_{}

Choose one answer.

A. Linearizing at and finding its root | ||

B. Bisecting the line from to | ||

C. Approximating with a Taylor polynomial of degree 2 at and finding its root | ||

D. Approximating with a Lagrange interpolator and finding its root | ||

E. None of the above |

Question
94

Let and . Use Newton's method to find .

Identify the approximation below that is correct to 6 significant digits.

Identify the approximation below that is correct to 6 significant digits.

Choose one answer.

A. | ||

B. | ||

C. | ||

D. | ||

E. |

Question
95

What do we mean when we say Newton's method is not a general purpose method?

Choose one answer.

A. It does not always converge. | ||

B. It may divide by zero. | ||

C. It requires the evaluation of f'. | ||

D. It may get stuck in a cycle. | ||

E. It requires complex arithmetic. |

Question
96

Which of the following is a Newton iteration to find ?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
97

Which of the following is a Newton iteration to find ?

Choose one answer.

A. | ||

B. | ||

C. | ||

D. |

Question
98

The secant method begins with two approximations,
and , to a zero of . The next point, is found by doing which of the following?

Choose one answer.

A. Using the secant angle between , and | ||

B. Averaging the Newton method and the bisection method | ||

C. Approximating with a Taylor polynomial of degree 2 at and finding its root | ||

D. Finding the x-intercept of the line joining and | ||

E. None of the above |

Question
99

The secant method requires how many function evaluations to complete k iterations?

Choose one answer.

A. k-1 | ||

B. k | ||

C. k+1 | ||

D. k+2 | ||

E. 2k |

Question
100

Let , and . Use the secant method to find . Identify the approximation below that is correct to 6 significant
digits.

Choose one answer.

A. | ||

B. | ||

C. | ||

D. | ||

E. |