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Calculus Overview
Calculus Overview
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1
The graph below shows the velocity of a runner on a straight path. How many times does the runner change directions?
5
4
3
6
2
\arcsin\left(x\right)=\frac{dx}{dy}\sin\left(x\right)
False
True
3
The third derivative is called "snap"
True
False
4
Speed Round (Basics 2/2): What's the significance of F\left(x\right), f^{-1}\left(x\right), and f'\left(x\right)?
Anti-derivative, Inverse, Derivative
Function of x, Inverse, Derivative
5
Calculus was, in part, created by Gottfried Wilhelm Leibniz
False
True
6
Find the y that satisfies (0, 2): \frac{dx}{dy}=4xy^3
y=\sqrt{\frac{1}{-4x^2+\frac{1}{4}}}
y=\sqrt{-4x^2+\frac{1}{2}}
y=\sqrt{\frac{1}{-4x^2+\frac{1}{2}}}
y=\sqrt{\frac{1}{-2\left(2x^2-\frac{1}{8}\right)}}
7
Which of the following are (some of) the rules of integration?
Product rule, Difference rule, Constant rule
Sum rule, Power rule, Indifference rule
Power rule, Substitution rule, Difference rule
Sum rule, Difference rule, Product rule
8
Slide Rules are used for functions such as trigonometry, logarithms, exponentiation, etc.
False
True
9
Find the absolute minimum: f\left(x\right)=3\sin\left(4x\right)-6x^2
x=0
x=-26
There is no absolute minimum
There is no absolute maximum
10
Which answer satisfies \frac{d^2x}{dy^2}-\frac{dx}{dy}=6y?
y=e^{3x}
y=2e^{2x}
y=\sin\left(3x\right)
y=2\sin\left(2x\right)
11
Speed Round (Terminology 4/4): Which cross-sectional has a volume formula of\frac{\sqrt{3}}{4}\int_a^b\left(x^2\right)dx
Equilateral Triangle
Rectangle
Isosceles Right Triangle (hypotenuse as base)
Semi-Circle
12
\pi\approx3.14119
False
True
13
The graph below shows the acceleration for the runner. On how many intervals is the runner's speed increasing?
4
5
7
6
14
Where is f\left(x\right)=\ln\left(x\right)-5e^x+9x^4 increasing?
(1, 1.174] U [1.587, 9.336)
(0, 0.174] U [0.587, 8.336]
(0, 0.174) U (0.587, 8.336)
[0, 0.174) U (0.587, 8.336)
15
Find the first derivative: x^4+12x^2-13x+1
4x^3+12x-13
4x^3+24x-13
4x^3+24x-12
x^3+24x-13
16
Find the first derivative: \tan\left(3x\right)
-3\csc^2\left(3x\right)
-3\sec^2\left(3x\right)
3\csc^2\left(3x\right)
3\sec^2\left(3x\right)
17
Solve the integral: \int_3^5\left(2x+7\right)dx
-30
-60
60
30
18
Calculus is Latin for "small pebble" because, in the past, pebbles were used for arithmetic functions.
False
True
19
Speed Round (Back to Basics 1/2): What is \sqrt{245} simplified?
5\sqrt{7}
7\sqrt{5}
20
Speed Round (Terminology 3/4): \pi\int_0^1\left(\left(x^2+1\right)^2\right)dx is an example of?
Square Cross-Sectionals
Rectangle Cross-Sectionals
Washer Method
Disc Method
21
Speed Round (Terminology 2/4): Which shows a particle slowing down?
v\left(t\right)<0 and a\left(t\right)<0
v\left(t\right)>0 and a\left(t\right)<0
v\left(t\right)<0 and a\left(t\right)>0
v\left(t\right)>0 and a\left(t\right)>0
22
Find the volume of the area R formed by f\left(x\right)=x^2 and g\left(x\right)=3x revolved around y=10.
\int_0^3\left(\left(10-x^2\right)^2-\left(10-3x\right)^2\right)dx
57.6
57.6\pi
180.956
23
{5 sec} Speed Round (Terminology 1/4): Which integral shows total distance traveled over [ a, b ]?
\int_b^a|v\left(t\right)|dt
\int_b^av\left(t\right)dt
\int_a^b|v\left(t\right)|dt
\int_a^bv\left(t\right)dt
24
Using square cross-sectionals, find the sum of the volumes of the areas made up by y=\sin\left(5x\right)+1 and y=-1.5x+2
1.162
0.162
1.665
0.665
25
Solve the integral: \int_{-3}^{-5}\left(3x^2+20x-3\right)dx
86
-68
-86
68
