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Calculus 1 Review Flashcards | StudBud
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Calculus 1 Review
Calculus 1 Review
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A review over limits, derivatives, and basic antiderivatives. #calculus
Flashcards
30 cards
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Answers
1
Use the Chain Rule to differentiate the function.
2zcos(z2)dz/dx
cos(z2)dz/dx
cos(z2)
sin(2z)dx/dz
2
Find the limit by visualizing the graph.
DNE
∞
-∞
0
3
Find
dy
/
dx
at the point (6, 6).
0
undefined
24
3/2
4
Describe the graph of the function below:
Top half of a circle with center (0, 1) and radius 9.
Top half of a circle with center (0, 1) and radius 3.
Top half of a circle with center (1, 0) and radius 3.
Top half of a circle with center (1, 0) and radius 9.
5
Find f
(4)
(0).
0
40
640
80
6
The velocity of a particle at time t, 0<t<6 is given by v(t). When does it change direction?
t = 3
t = 4
t = π/3
t = 3π
7
What is the
x
-coordinate of the point of inflection of the equation below?
-3
9
3
-9
8
Find f(x) given the information below.
f(x) = 12x - 22
f(x)=2x3-(3/2)x2-8
f(x)=2x3-(3/2)x2 + 2
f(x) = 12x - 3
9
Find the limit. Factor and use property: lim of a (product)=product of the limits
5
DNE
-∞
∞
10
Find dy/dx using implicit differentiation.
dy/dx = 3x2/(3y2 - 8e2y)
dy/dx = (3y2 - 8e2y)/3x2
dy/dx = 8e2y/(3x2 + 3y2)
dy/dx = 8e2y/3x2
11
Find the derivative.
3x2/√(1 + x6)
-1/√(1 + x5)
1/√(1 + x6) + C
1/(1 + x6)
12
Find f'(x).
2cot(2x)
1/cos(2x)
2tan(2x)
2/sin(2x)
13
Find the Vertical and Horizontal Asymptotes, respectively.
x = 7, x = -3, y = 0
x=1, y = 0, y = 4
x=0, y = 7, y = -3
x = -7, x = 3, y = 0
14
Find f'(x).
2x sin x2
-sin x2
-2x sin x2
2 cos x
15
Evaluate the indefinite integral. Possibly more than one correct answer. Check all that apply.
2sin-1(x) + C
2sin-1(x/2) + C
2sec-1(x) + C
-2cos-1(x/2) + C
16
Find all vertical asymptotes of the function below.
x = -5 only
x = -1 only
x = 2 and x = -5
x = 2 only
17
Find the limit.
-∞
-5
5
∞
18
Evaluate:
-3
3
4
0
19
Evaluate the definite integral.
1/4 ln(4 + e4x) + C
ln|4 + e4x|+ C
1/4 ln|4 + e4x|+ C
1/2 tan-1(e2x/2) + C
20
Find the limit.
5
∞
10
-∞
21
Evaluate:
5/8
-5/8
1
DNE
22
Which statement about f(x) is true when x = -1?
f is neither continuous nor differentiable.
f is continuous but not differentiable
f is both continuous and differentiable.
f is differentiable but not continuous
23
Find the limit. Think of the graph :)
-∞
DNE
0
∞
24
Find f'(x).
2 cos x
-sin 2x
2 sin x
-2 cos x sin x
25
Evaluate the indefinite integral.
esinx
etanx + C
esinx + C
ecosx +C
26
Use the Chain Rule to differentiate the function.
8pdp/dz
8pln(8)dp/dz
8pln(p)dp/dz
8pln(8)dz/dp
27
Find dx/dt at the instant s = 10 mi.
-400 mi/hr
400 mi/hr
-500 mi/hr
500 mi/hr
28
Find f'(x).
cos 2x
cos2 x + sin2 x
cos2 x - sin2 x
-sin x cos x
29
Find dy/dx.
10e2xsin4(e2x)cos(e2x)
-10e2xsin4(e2x)cos(e2x)
5cos4(e2x)
10sin4(e2x)cos(e2x)
30
Given f(x), find f'(π).
-2π - 4
0
-1
-2π + 4
