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ap calc project
ap calc project
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Answers
1
Find f
'
(2) of this function:
362.5
1451.5
0
1452
2
What does the Fundamental Theorem of Calculus connect?
Differentiation and Integration
Series and Sequences
Functions and their Inverses
Limits and Continuity
3
What are the horizontal asymptote(s) of this function?
x=-2
x=3
x=2, x=-2
x=3, x=2
4
True or false: If a function is continuous it must be differentiable
True
False
5
Find the indicated limit:
2/5
2
x2
∞
6
Find the integral of this function:
\frac{1}{2}\sin^{-1}\left(x^2\right)+c
\frac{1}{2}\tan^{-1}\left(x^2\right)+c
\frac{1}{2}\tan^{-1}\left(x^2\right)
2\tan^{-1}\left(x^2\right)+c
7
Which of the following best describes the continuity of this function at x=3?
jump discontinuity
it's continuous at x=3
infinite discontinuity
removable discontinuity
8
What does the first derivative mean the same thing as?
Concavity of the original function
Slope of the tangent line
Slope of the normal line
The area under the curve
9
The derivative of which function is itself?
x
ex
tan(x)
ln(x)
10
What is the limit?
1/4
2/3
0
DNE
11
On what intervals is
h
increasing if h\left(x\right)=\int_3^xg\left(t\right)dt and shows the continuous graph of
g
?
[2,5]
\left[0,1\right]∪\left[3,7\right]
\left[1,3\right]∪\left[7,8\right]
\left[1,7\right]
12
True or false: If function
f
has a derivative at x=a, then
f
is continuous at x=a
True
False
13
Evaluate this indefinite integral:
2\csc\left(2x\right)+c
-2\csc\left(2x\right)+c
-\frac{1}{2}\cot\left(2x\right)+c
-2\cot\left(2x\right)+c
14
Take a guess: Who formalized the definition of a limit that is used in calculus today?
Leonhard Euler
Gottfried Leibniz
Bernhard Riemann
Augustin-Louis Cauchy
15
Find the equation of the tangent line of the given equation through the point (1,3):
y-3=3\left(x-1\right)
y-3=-3\left(x-1\right)
y-3=-\frac{1}{3}\left(x-1\right)
y-1=-3\left(x-3\right)
16
How do you find horizontal tangent lines?
Find where the derivative is negative
Find where the derivative equals 1
Find where the derivative equals zero
Find where the derivative is undefined
17
Take a guess: Who is one of the mathematicians credited with the development of calculus?
Pythagoras
Albert Einstein
Carl Friedrich Gauss
Isaac Newton
18
Take a guess: Who developed the notation for derivatives such as \frac{dy}{dx} and \frac{d^2y}{dx^2}?
Augustin-Louis Cauchy
Gottfried Leibniz
Bernhard Riemann
Leonhard Euler
