408 STEP 5. Build Your Test-Taking Confidence
- What is the value of
∑∞
n= 0
1
(n+ 2 )(n+ 3 )
?
(A)
1
6
(B)
1
3
(C)
1
2
(D) 2
y
f
0 x
1
- The domain of the functionf is 0≤x≤9as
shown above. Ifg(x)=
∫x
0
f(t)dt, at what
value ofxisg(x)the absolute maximum?
(A) 0
(B) 1
(C) 2
(D) 8
- Which of the following represents the arc
length of the curve with the parametric
equationsx=
√
tandy=etfor 4≤t≤9?
(A)
∫ 9
4
(√
t+et
)
dt
(B)
∫ 9
4
√
t+e^2 tdt
(C)
∫ 9
4
(
1
2
√
t
+e^2 t
)
dt
(D)
∫ 9
4
√
1
4 t
+e^2 tdt
- If f(x)=
3 x
1 + 2 x
, the horizontal asymptotes of
the graph off is/are
(A) y=
3
2
only
(B) y=0 only
(C) y=0 andy=
3
2
(D) nonexistent
- Which of the following expressions gives the
slope of the tangent line to the curve of the
polar equationr=2 cosθatθ=
π
3
?
(A) −2 sin
(
π
3
)
(B)
−2 sin
(
π
3
)
cos
(
π
3
)
−2 cos
(
π
3
)
sin
(
π
3
)
−2 sin
(
π
3
)
sin
(
π
3
)
+2 cos
(
π
3
)
cos
(
π
3
)
(C)
−sin
(
π
3
)
sin
(
π
3
)
+cos
(
π
3
)
cos
(
π
3
)
−sin
(
π
3
)
cos
(
π
3
)
−cos
(
π
3
)
sin
(
π
3
)
(D)
−2 sin
(
π
3
)
sin
(
π
3
)
+2 cos
(
π
3
)
cos
(
π
3
)
−2 sin
(
π
3
)
cos
(
π
3
)
−2 cos
(
π
3
)
sin
(
π
3
)
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