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