Chap 26 Review

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

Exercise 1 In the polynomial \(a_0 + a_x x + a_y y + a_{xy} xy\), what is the term \(a_{xy}xy\) called?

Interaction term       Quadratic term       Linear term       Constant term      

question id: Poly01

Exercise 2 In the polynomial \(a_0 + a_x x + a_y y + a_{xx} xx\), what is the coefficient on the interaction term?

0       \(a_{xy}\)       \(a_{xx}\)       \(a_0\)      

question id: Poly02

Exercise 3 Imagine a second-order polynomial in three inputs: \(x\), \(y\), and \(z\), like this: \[b_0 + b_x x + b_y y + b_z z + b_{xy} xy + b_{xz} xz + b_{xx} x^2 + b_{yy} y^2 + b_zz z^2\ .\] All of the possible second-order (or less) terms are shown, except for one. Which term is missing?

the interaction between \(y\) and \(z\)

the quadratic term in \(z\)

the linear term in \(y\)

the constant term

question id: Poly03

Exercise 4 Here is a function \(f(x)\):

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: Poly04

Exercise 5 Here is a function \(f(x)\):

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: Poly05

Exercise 6 Here is a function \(f(x)\):

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: Poly06

Exercise 7 Here is a function \(f(x)\):

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: Poly07

Exercise 8 Here is a function \(f(x)\):

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: Poly08

Exercise 9 Here is a function \(f(x)\):

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: Poly09

Exercise 10 Here is a function \(f(x)\):

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: Poly10

Exercise 11 Here is a function \(f(x)\):

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: Poly11

Exercise 12 Here is a function \(g(x)\):

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: Poly12

Exercise 13 Here is a function \(g(x)\):

with a Taylor polynomial shown in magenta. What is the order of the polynomial?

zero       one       two       three       four      

question id: Poly13

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