MA 3972-MA-Book April 11, 2018 16:20
394 STEP 5. Build Your Test-Taking Confidence
- The correct answer is (D).
[0, π] by [–2, 2]
Using the [Inflection] function of your calculator,
you will find three points of inflection. They
occur atx= 1 .335, 2.195, and 2.8.
- The correct answer is (D).
∫ 10
4
f(x)dx≈ 2 (f( 6 )+ f( 8 )+ f( 10 ))
≈ 2 ( 2. 4 + 2. 8 + 3. 2 )≈ 16. 8
- The correct answer is (D).
f(−1) = 2 ⇒ a point (−1, 2).
f′(− 1 )=
1
2
⇒ the slope atx=−1is
1
2
.
Equation of tangent atx=−1is
y− 2 =
1
2
(x+ 1 )ory=
1
2
(x + 1 )+2.
Thus,f(− 1. 1 )≈
1
2
(− 1. 1 + 1 )+ 2 ≈ 1 .95.
- The correct answer is (C).
Area=
∫b
1
lnx
x
dx= 0. 66.
Letu=lnx; du=
1
x
dx.
∫
lnx
x
dx =
∫
udu=
u^2
2
+C=
(lnx)^2
2
+C
∫b
1
lnx
x
dx=
(lnx)^2
2
]b
1
=
(lnb)^2
2
−
(ln 1)^2
2
=
(lnb)^2
2
Let
(lnb)^2
2
= 0 .66, (lnb)^2 = 1. 32.
lnb=
√
1. 32
elnb=e
√
1. 32
b≈ 3. 15
- The correct answer is (B).
0
2
y = – 4 – x^2
y = 4 – x^2
y
x
Area of a cross section=
1
2
π
(√
4 −x^2
) 2
=
1
2
π
(
4 −x^2
)
.
Volume of the solid=
∫ 2
− 2
1
2
π
(
4 −x^2
)
dx.
Using your calculator, you obtainV=
16 π
3
.
- The correct answer is (A).
Temperature of coffee
= 95 −
∫ 5
0
4 sin
(
t
4
)
dt
≈ 95 − 10. 9548 ≈ 84 ◦Fahrenheit.
