Chap 26 Review

\[ \newcommand{\dnorm}{\text{dnorm}} \newcommand{\pnorm}{\text{pnorm}} \newcommand{\recip}{\text{recip}} \]

Exercise 1 Refer to Figure 1 when answering the following questions:

Figure 1: The function \(f(x)\)
  1. Consider Figure 1 In the Taylor polynomial approximation to \(f(x)\) centered at \(x=-2\), what will be the sign of the coefficient on the first-order term. Choose the best answer.
positive       zero       negative       no such coefficient exists in a Taylor polynomial      

question id: poly-91-1

Note, you can hover over the link Figure 1 to the figure to pop it up for reference.

  1. Consider Figure 1. In the Taylor polynomial approximation to \(f(x)\) centered at \(x=1\), what will be the sign of the coefficient on the first-order term. Choose the best answer.
positive       zero       negative       no such coefficient exists in a Taylor polynomial      

question id: poly-91-2

  1. Consider Figure 1. In the Taylor polynomial approximation to \(f(x)\) centered at \(x=1\), what will be the sign of the coefficient on the second-order term. Choose the best answer.
positive       zero       negative       no such coefficient exists in a Taylor polynomial      

question id: poly-91-3

  1. Consider Figure 1 In the Taylor polynomial approximation to \(f(x)\) centered at \(x=-4\), what will be the sign of the coefficient on the first-order term. Choose the best answer.
positive       zero       negative       no such coefficient exists in a Taylor polynomial      

question id: poly-91-4

  1. Consider Figure 1 In the Taylor polynomial approximation to \(f(x)\) centered at \(x=4\), what will be the sign of the coefficient on the second-order term. Choose the best answer.
positive       zero       negative       no such coefficient exists in a Taylor polynomial      

question id: poly-91-5

  1. Consider Figure 1 In the Taylor polynomial approximation to \(f(x)\) centered at \(x=4\), what will be the sign of the coefficient on the constant (zeroth-order) term. Choose the best answer.
positive       zero       negative       no such coefficient exists in a Taylor polynomial      

question id: poly-91-6

  1. Consider Figure 1 In the Taylor polynomial approximation to \(f(x)\) centered at \(x=3\), what will be the sign of the coefficient on the second-order term. Choose the best answer.
positive       zero       negative       no such term exists in a Taylor polynomial      

question id: poly-91-7

8, Consider Figure 1. In the Taylor polynomial approximation to \(f(x)\) centered at \(x=0\), what will be the sign of the coefficient on the reciprocal term. Choose the best answer.

positive       zero       negative       no such term exists in a Taylor polynomial      

question id: poly-91-8

Exercise 2  

Figure 2: The function \(g(x)\).

Consider Figure 2. Two Taylor polynomials centered on the same \(x\) are shown. One is fifth-order, the other is third-order. Which is which?

The third-order polynomial is brown.

The third-order polynomial is magenta.

question id: drill-Polynomials-12

Exercise 3  

Figure 3: Function \(g()\).

Consider Figure 3 which includes a Taylor polynomial shown in magenta. What is the order of the polynomial?

zero       one       two       three       four      

question id: drill-Polynomials-13

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