MATH 141 Midterm: MATH141 Exam 1 2017 Spring Sample B Question
MATH 141 EXAM I SAMPLE B
1. Suppose g=f−1is the inverse of a differentiable function fsuch
that
f(1) = 3, f(2) = 1, f(3) = −2, f0(1) = −2, f0(2) = −3, f0(3) = 1.
Which one of the following is equal to g0(3)?
a) −1
2
b) 1
2
c) 1
d) 2
e) −1
2. Evaluate lim
x→1
2
+
ln(4x−2).
a) 0
b) ∞
c) −∞
d) 1
e) e
3. If f(x) = ln(x2sin x) find f0(x).
a) f0(x) = xcos x+ 2 sin x
xsin x
b) f0(x)=2xcos x
x2sin x
c) f0(x)=1
x2sin x
d) f0(x)=2sin x−xcos x
xsin x
e) f0(x)=2cos x+xsin x
xcos x
4. Evaluate the integral Z2
1
4 + x2
x3dx.
a) 4+ ln 2
b) 3
2+ln 2
c) −3 ln 2
d) 4 ln 2
e) 1
2+ln 2
5. Differentiate the function y=e5 sec √x.
a) y0=e5 sec √xsec √xtan √x
2√x
b) y0=−tan2x·e5sec √x
c) y0=2e5sec √x·sec √xtan √x
√x
d) y0=5e5sec √x
2√x·sec √xtan √x
e) y0=−5e5sec √xtan2x
6. If f(x) = 3x, find the second derivative f00(x).
a) f00(x) = 3x
b) f00(x) = x(x−1)3x−2
c) f00(x) = 2 ln 3 ·3x
d) f00(x) = (ln(3))23x
e) f00(x) = 3x
2ln 3
7. If f(x) = x2x, find f0(e).
a) 2e2e
b) 4
c) 1
d) 2e2
e) 4e2e
8. The function f(x) = ln |ln |t|| +Cis equal to which one of the
following?
a) Zln t
tdt
b) Zln t
t2dt
c) Zln tdt
d) Z1
tln tdt
e) Zln t
tdt
1
Document Summary
Sample b: suppose g = f 1 is the inverse of a di erentiable function f such that f (1) = 3, f (2) = 1, f (3) = 2, f(cid:48)(1) = 2, f(cid:48)(2) = 3, f(cid:48)(3) = 1. Which one of the following is equal to g(cid:48)(3): 1. 2: 1, 2, 1, evaluate lim x 1. 2 ln(4x 2): 0, 1, e x, di erentiate the function y = e5 sec x tan x x sec. 2: y(cid:48) = e5 sec x, y(cid:48) = tan2 x e5 sec x x sec x, y(cid:48) = 2 sin x x cos x x sin x. 1 x3: evaluate the integral, 4 + ln 2. + ln 2 b: 3 ln 2, 4 ln 2 e) + ln 2: 2e2e, 4, 1, 2e2, 4e2e (cid:90) (cid:90) (cid:90) (cid:90) (cid:90) ln t t ln t t2 dt dt ln tdt.
