Chap 27 Review

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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.

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

27-review.rmarkdown

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