376 STEP 5. Build Your Test-Taking Confidence
- What is lim
Δx→ 0
sin
(
π
3
+Δx
)
−sin
(
π
3
)
Δx
?
(A) −
1
2
(B) 0
(C)
1
2
(D)
√
3
2
- Ifx=costandy=sin^2 t, then
d^2 y
dx^2
att=
π
4
is
(A)
√
2
(B) − 2
(C) 1
(D) 0
- Iff(x) is an antiderivative ofxe−x^2 and
f(0)=1, then f(1)=
(A)
1
e
(B)
1
2 e
−
3
2
(C)
1
2 e
−
1
2
(D) −
1
2 e
+
3
2
y
a x
0 b
f
- The graph of the function fis shown above.
Which of the following statements is/are true?
I. f′(0)= 0
II. fhas an absolute maximum value
on [a,b]
III. f′′<0on(0,b)
(A) III only
(B) I and II only
(C) II and III only
(D) I, II, and III
7.
∑∞
n= 1
1
(2n−1)(2n+1)
=
(A)
1
2
(B) 1
(C) 0
(D) 4
- Which of the following series are convergent?
I. 12 − 8 +
16
3
−
32
9
+···
II. 5 +
5
√
2
2
+
5
√
3
3
+
5
2
+
√
5 +
5
√
6
6
+···
III. 8 + 20 + 50 + 125 +···
(A) I only
(B) II only
(C) III only
(D) I and II
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