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Review of Calculus
Review of Calculus
20 terms
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Derivatives & Antiderivatives
Flashcards
20 cards
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Practice quiz
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Questions
20
Answers
1
lim x→0 e
x
cos(x)/4=
½
0
-¼
¼
2
Using Direct Substitution, solve lim x→3 ½ x
2
- 2x+ 3
2.5
1.5
3.5
5.5
3
What type of Riemann's Sum is this?
LRAM
Midpoint
Trapezoidal
RRAM
4
What is the derivative of x
5
-4x
4
+3?
1/6x6-4/5x5+3/2x2+c
1/5x5-1/4x4+3x
5x4-16x3+0
1/6x6-4/5x5+3/2x2
5
lim x→0 1-cos(x)/x=
1
-1
0
sin(x)
6
The first step of "Problem solving strategy for applied minimum and maximum problems" is
Sketch a picture and identify quantities known/unknown
Write the secondary equation
Write the primary equation
Determine the quantity that is to be minimized or maximized
7
What is this symbol called: ∫ ?
Integration symbol
Integrand symbol
Antiderivative
Derivative
8
What is NOT a rule for definite integrals?
constant multiples cannot be moved outside
intervals can be added or subracted
Reversing the limits change the sign
If the upper and lower limits are =, then the integral is 0
9
What is NOT part of The Fundamental Theorem of Calculus?
f is any derivative of f on [a,b]
f is continuous at every point of [a,b]
F(b)-F(a)
F is any antiderivative of f of [a,b]
10
If distance is in feet then velocity and acceleration should be in:
velocity: feet/sec acceleration: feet/second
velocity: feet/sec acceleration: feet/second2
velocity: feet acceleration: seconds
velocity: seconds acceleration: feet
11
lim x→0 sin(x)/x =
-cos(x)
cos(x)
0
1
12
What is an indeterminate?
Leading to a definite end result (an answer)
Not leading to a definite end or result (0/0 or inf/inf)
13
What is a continuous function?
Oscillating continuity
Infinite continuity
Jump continuity
None of the above
14
Where does the limit exist?
lim x→ -1
lim x→ -4
lim x→ 2
lim x→ 4
15
True or False? The Trapezoidal Rule gives us a better approximation than Right/Left rectangles.
True
False
16
What is the derivative of log
a
x?
u*ln(a)
a/ln(u)
u/ln(a)
1/u*ln(a)
17
Velocity is the derivative of:
position
acceleration
velocity
speed
18
What is the formula for derivative of an inverse?
f'(x)=g'(h(x))(h'(x))
h'(x)=(g(x)f'(x)-f(x)g'(x))/[g(x)]2
h'(x)=f(x)g'(x)+g(x)f'(x)
[f'(x)]'=1/f'(f-1(x))
19
Which derivatives fail to exist?
Cusp
Corner
Discontinuity
Vertical Tangent
20
Antiderivative of sin(x)
cos(x)
cos(x)+c
-cos(x)+c
-cos(x)
