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Calculus Review
Calculus Review
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1
Technique to evaluate limits of indeterminate forms usually used in Calculus
LaPLace Transformations
L'Hopital Rule
Tessellation
Least Squares Method
2
Evaluating Limits:
-4
1
0
-3
3
Derivative of constant value
x
1
0
C
4
Integral Rules
(D)
(C)
(B)
(A)
5
The Exponentials Derivative
ekx
keex
eex
kekx
6
Trig Derivatives
-csc (x) cot (x)
sec (x) tan (x)
-csc2 (x)
sec2 (x)
7
When is your exam?
Tuesday May 13th, 8 am
Monday May 12th, 8am
Wednesday May 14th 8 am
Friday May 8th, 8 am
8
In the U-substitution Method, what is U?
cos(x)
ex
sin(ex)
sinx
9
Trig Derivatives
sec2 (x)
-csc2 (x)
sec (x) tan (x)
-csc (x) cot (x)
10
Integral Rules
(B)
(C)
(D)
(A)
11
Continuity implies differentiability
False
True
12
How do you find critical values without a calculator
antiderivative equal to zero
you can't find them without a calculator
first derivative equal to zero
second derivative equal to zero
13
What is the chain rule for derivatives?
f'(x) = f(x)*g'(x) + g(x)*f'(x)
f'(x) = [g(x)*f'(x) - f(x)*g'(x)] / g2(x)
f'(x)=nx(n-1)
f'(x) = f'(g(x))*g'(x)
14
Integral Rules 9:
-tan2(x) + C
csc x + C
csc2(x) + C
-csc x + C
15
Q13: Evaluating Limits
infinity
7/3
0
3
16
Trig Derivatives
sin (x)
- sin (x)
sec (x)
- sec (x)
17
Integral Rules
(C)
(A)
(B)
(D)
18
Evaluating limits
-2
Does not exist
∞
2
19
when evaluating overall limits
DNE
the left limit has to equal the right limit, or else its DNE
the y-value of the point with a closed circle
it's always 0
20
Trig Derivatives
-csc (x) cot (x)
sec2 (x)
sec (x) tan (x)
-csc2 (x)
21
Derivative Rules
False
True
22
Trig Derivatives
-csc (x) cot (x)
sec2 (x)
- csc2 (x)
sec (x) tan (x)
23
Derivative Rules
True
False
24
Derivative Rules: What is the derivative of ln(5x)
\frac{1}{5x}
5\ln\left(5x\right)
\frac{1}{\ln\left(5x\right)}
\frac{1}{x}
25
A normal line is the perpendicular line to the tangent at the same point
True
False
26
What is the difference between average and instantaneous rate of change?
avg is at one moment, inst. is over an interval
there is no difference
ugh idk
avg is over an interval, inst. is at one moment
27
Derivative Rules
True
False
28
What is NOT needed to prove if a function f is continuous at x=a
f(a) is equal to the limit at x=a
overal limit at x=a exists
f(x) has a critical value at x=a
f(a) is defined
29
The Product Rule Derivative
fg' + f'g
f'g + f'g
fg
f' + g'
30
What is the quotient rule for derivatives?
f'(x) = f'(g(x))*g'(x)
f'(x) = [g(x)*f'(x) - f(x)*g'(x)] / g2(x)
f'(x) = f(x)*g'(x) + g(x)*f'(x)
f'(x)=nx(n-1)
31
Integral Rules 13:
-cot x + C
sec x + C
-sec x + C
cot x + C
32
What are limits when referring to calculus?
a point/level beyond something that may not extend or pass
the value that a function or sequence approaches some value
the value of a function or sequence that goes on to infinity
all of the above
33
General Power Rule Derivative
nxn-1
xn-1
nx-1
n-1nx
34
Integral Rules
(D)
(C)
(B)
(A)
35
what is a derivative?
average rate of change
any slope
slope of the tangent line
slope of secant line
36
Trig Derivatives
-cos (x)
csc (x)
cos (x)
- csc (x)
37
What are the types of discontinuities?
infinite
jump
removable
all of these
38
Integral Rules
(A)
(B)
(D)
(C)
39
Integral Rules 1:
log|x| + C
sec(x) + C
ln|x| + C
tan(x) + C
