9.7 Taylor Polynomials and Approximations 547
9.7 Taylor Polynomials and Approximations
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find a first-degree polynomial function P1 whose value and slope agree with the
value and slope of at .
a.
b.
c.
d.
e.
____ 2. Use a graphing utility to graph and P1, a first-degree polynomial
function whose value and slope agree with the value and slope of f at .
a.
d.
548 Chapter 9: Infinite Series
b.
e.
c.
____ 3. Find a first-degree polynomial function P1 whose value and slope agree with the
value and slope of f at . What is P1 called?
a. tangent line to at
b. secant line to at
c. secant line to at
d. secant line to at
e. tangent line to at
9.7 Taylor Polynomials and Approximations 549
____ 4. Find a first-degree polynomial function P1 whose value and slope agree with the
value and slope of f at . What is P1 called?
a. ; tangent line to at
b. ; secant line to at
c. ; tangent line to at
d. ; differential of at
e. ; tangent line to at
____ 5. What is a first-degree polynomial function whose value and slope agree with the
value and slope of at ?
a.
is the tangent line to the curve at the point
b.
is the tangent line to the curve at the point
c.
is the tangent line to the curve at the point
d.
is the tangent line to the curve at the point
e.
is the tangent line to the curve at the point
____ 6. Consider the function and its second-degree polynomial
at Compute the value of and Round
your answer to four decimal places.
a.
b.
c.
d.
e.
550 Chapter 9: Infinite Series
____ 7. Find the Maclaurin polynomial of degree 4 for the function.
a.
b.
c.
d.
e.
____ 8. Find the Maclaurin polynomial of degree 3 for the function.
a.
b.
c.
d.
e.
____ 9. Find the Maclaurin polynomial of degree 5 for the function.
a.
b.
c.
d.
e.
9.7 Taylor Polynomials and Approximations 551
____ 10. Find the Maclaurin polynomial of degree 4 for the function.
a.
b.
c.
d.
e.
____ 11. Find the fourth degree Maclaurin polynomial for the function.
a.
b.
c.
d.
e.
____ 12. Find the Maclaurin polynomial of degree two for the function .
a.
b.
c.
d.
e.
552 Chapter 9: Infinite Series
____ 13. Find the third Taylor polynomial for expanded about .
a.
b.
c.
d.
e.
____ 14. Find the third degree Taylor polynomial centered at for the function.
a.
b.
c.
d.
e.
____ 15. Find the fourth degree Taylor polynomial centered at for the function.
a.
b.
c.
d.
e.
____ 16. Determine the degree of the Maclaurin polynomial required for the error in the
approximation of the function to be less than 0.001.
a.
b. 2
c. 5
d. 1
e. 3
9.7 Taylor Polynomials and Approximations 553
____ 17. Determine the values of x for which the function can be replaced by the
Taylor polynomial if the error cannot exceed 0.008. Round your answer to four
decimal places.
a.
b.
c.
d.
e.
554 Chapter 9: Infinite Series
9.7 Taylor Polynomials and Approximations
Answer Section