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