Larson_Calculus_10e ch09sec07
MULTIPLE CHOICE
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.
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
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.
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.
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.
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
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.