416 STEP 5. Build Your Test-Taking Confidence
- The Maclaurin series given below for the
functionf(x)=tan−^1 xis
tan−^1 x=x−
x^3
3
+
x^5
5
−···+(− 1 )n+^1
x^2 n−^1
2 n− 1
.
(A) Ifg(x)= f′(x), write the first four
non-zero terms of the Maclaurin series for
g(x).
(B) Ifh(x)=f( 2 x), write the first four
non-zero terms and the general term of the
Maclaurin series forh(x).
(C) Find the interval of convergence for the
Maclaurin series forh(x).
(D) The approximate value ofh
(
1
4
)
is
11
24
using the first two non-zero terms of the
Maclaurin series. Show that
∣∣
∣
∣h
(
1
4
)
−
11
24
∣∣
∣
∣
is less than
1
150
.
STOP. AP Calculus BC Practice Exam 2 Section II Part B
