stud
bud
Sign up
Log in
Home
Library
Explore
SAT
More
AP Claculus Flashcards | StudBud
Explore
/
AP Claculus
AP Claculus
41 terms
·
StudBud Administration
·
29 plays
You already know who it is
Flashcards
41 cards
F
Practice quiz
P
Host live
L
Questions
41
Answers
1
derivative of sin
-1
(x)
-1/√1-x2
1/√1-x2
1/1+x2
-cos(x)
2
What is the derivative of tan(x)?
sec2(x)
sin(x)cos(x)
sec(x)
-cos(x)
3
Derivative of cot(x)?
-csc2(x)
sec(x)cot(x)
tan2(x)
csc(x)
4
The velocity changes sign from + to - at x = 2
Neither
Local minimum
Local maximum
5
For a point on a function to be continuous
f(a) exists
It has no cusps
Limit as x approaches a of f(x) equals the value of f(a)
Limit as x approaches a of f(x) exists
6
Any discontinuitys for the function (x+3)/(x+2)(x+3)
Yes, jump discontinuity at x = -2
No, Continuous everywhere
Yes, hole at x = -3
Yes, vertical assyptote at x = -2
7
How is an integral related to a limit
They are the same
An integral is the limit of a remain sum as n approaches ∞
Integrals have infinite "rectangles"
An integral is the limit of a remain sum as ΔX approaches 0
8
What is the limit at x = 5
DNE
10
Not enough information
10.1
9
Derivative of csc(x)?
cot(x)csc(x)
sec2(x)
sin2(x)
-csc(x)cot(x)
10
Position, Velocity, Aceleration
Bertha's movements
Distance vs. speed vs. IROC
Anti-derivatives of each other respectively
Derivatives of each other respectively
11
What is the second derivative of 3x
4
-2x
36x2
36x3-1
12x3-2
12x3
12
Derivative of e
x
ex
eu
ex
exln(e)
13
Derivative of cos
-1
(x)
1/1+x2
1/√1-x2
sec(x)
-1/√1-x2
14
How does the second derivative represent concavity
If f''(t) is negative the function is concave down
f''(t) gives the concavity of velocity
If f''(t) is positive the function is concave down
The sign of f''(t) corresponds to concavity
15
Contestants, find the limit of this equation: (ln(1-x)-sin(x))/1-cos
2
x
1
⫪/4
-1
The limit does not exist
16
What is the derivative of -2/x
3
-6x4
6x-4
-12x-2
ln|x3| -2
17
How would you find a point of inflection
Integrating with respect to f(t)
Checking for a sign change in the second derivative
Canditates test
Same process as finding a max or min
18
How are acceleration and velocity related
An acceleration graph shows the concavity of velocity
Acceleration is the anti-derivative of velocity
v'(t) = a(t)
Acceleration represents how velocity is changing
19
What is an IROC?
A secant line
The international rate of change
The derivative of a function
The average rate of change between two points.
20
Any discontinuitys for the function (1)/(x+1) ?
Yes, a hole at x= -1
Yes, cusp at x = -1
Yes, vertical assymptotes at x = -1
No, continuous everywhere
21
When Would L'Hopitals rule apply
It is essentially the chain rule for integrals
It is a way to differentiate a cusp
A limit evaluated at a point turns up an indeterminate form
When the denominator of a function is 0
22
What is the derivative of sec(x)?
sec(x)tan(x)
cot2(x)
cos(x)
tan2(x)
23
How would you achieve critical numbers?
Set f'(t) = 0
Set f''(t) = 0
Candidates test
Set velocity equal to zero
24
Derivative of tan
-1
(x)
cotan(x)
1/1+x2
1/√1-x2
-1/√1-x2
25
What is a Limit?
A derivative
An unreachable bound
The value of a function at a point
What the value a function approaches at a point
26
What is the limit definition of a derivative
limit as h approaches 0 of f(a+h)-f(a)/h
The function has to be differentiable
Cusps are not differentiable
The slope as the change in x approaches 0 between two points
27
When would you use the quotient rule?
When integrating with respect to y
When you want to derive a fractional function
When you want to derive a product of functions
When U substitution does not work
28
One last question, breathe
Orange
Green
Red
Blue
29
To test for local extrema you would...
Find the maximum value of the derivative
Check endpoints
Candidate's test
Find critical numbers
30
Quick breather before some more derivatives, What is Holden's middle name
Kurtis
Josh
Brad
Micheal
31
What is an AROC?
The instantaneous rate of change
Average rate of change
The derivative of a function
The slope of a secant line
32
What is a normal line?
The line perpendicular to a tangent line
y = mx + b
The tangent line
The limit of a secant line
33
What counts as a critical number?
The velocity being zero
The velocity at its min point
The velocity being undefined
The velocity at its max point
34
Derivative of a
x
ax
ax ln(a)
ln|a| * x
ax
35
Now what? (whatchu gon do with the crity numeros?)
Line test to see if the derivative changes sign
Graph them
Plug them back into the function
Plug them into the second derivative
36
What does the sign of a derivative represent?
Up or down
The speed at which position is changing
Whether a function is increasing or decreasing
Concavity
37
What is the derivative of x
2
tan(x)
2xsec2(x)
2xtan(x) + x2sec2(x)
Indeterminate
x2tan(x) + x22sec2(x)
38
How does speed relate to velocity
|v(t)| = s(t)
Speed is the derivative of velocity
Speed is the absolute value of aceleration
v'(t) = s(t)
39
How do Integration and Differentiation relate
Opposite operations of each other as dmnstrtd by the 2nd FTC
They are derivatives of eachother
Velocity vs. aceleration
They are synonymous with calculus
40
How do you derive on the calculator active part of the test
There is no differentiation for integrals
Nderive function
Quotient rule
Math 8!
41
What even is a derivative?
The slope at a single point
The rate at which a function is changing
f'(x)
Velocity to position
