Particle P moves along a line according to s=f(t). If s is the position of P on the line at time t, which is true?

The velocity v of P at time t is given by \frac{ds}{dt}.

If you find the derivative of the outside function and then multiply by the derivative of the inside one, you are ____.

using the Chain Rule to differentiate a composite function

If a first-order differential equation in x and y is separable, how can that d.e. be written?

All y-terms are on one side of the equation. All x-terms are on the other.

If the function y=f(x) is integrable on the interval a\le x\le b, then \frac{1}{b-a}\int_a^bf(x)dx=

the average value of f from a to b

Which of these functions is NOT continuous at each real number in its domain?

a rational function at a value that makes the denominator equal to 0

Which of the following is NOT true of the second derivative of a function?

It helps you calculate the area under a function.

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AP Calculus AB

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Are you the absolute best at AP Calculus AB? Is problem-solving your area of expertise? Put your knowledge to the test with this cumulative Barron's quiz developed from our must-have AP® Calculus Premium study guide. #apcalculus #apcalculusab #calculus #calculusab #apcalc #apcalcab #calc #calcab #math #highschool #grade10 #grade11 #grade12 #apexam #apreview #apprep AP® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product.

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Questions 15

Answers

1
Particle P moves along a line according to s=f(t). If s is the position of P on the line at time t, which is true?
The acceleration a of P at time t is given by \frac{ds}{dt}.
The velocity v of P at time t is given by \frac{ds}{dt}.
The velocity v of P at time t is given by \frac{dv}{dt}.
The speed of the particle is 2v.
2
If f is continuous on a closed interval [a,b] and F'=f, what is true according to the Fundamental Theorem of Calculus?
f'(c)=\frac{f(a+b)-f(a)}{b}
(f\circ a)(b)=f(a(b))
\int_a^bf(x)dx=F(b)-F(a)
\frac{f(b)-f(a)}{b-a}=f'(c)
3
Which theorem relates average rate of change and instantaneous rate of change and has Rolle's Theorem as a special case?
Extreme Value Theorem
Sandwich Theorem
Mean Value Theorem
Intermediate Value Theorem
4
If the region bounded by y=x^2,x=2,and y=0 is rotated about x=2, this finds the volume of the solid generated.
symmetry method
cross section method
disk method
general solution method
5
If you find the derivative of the outside function and then multiply by the derivative of the inside one, you are ____.
using the Chain Rule to differentiate a composite function
making a mistake in your calculations
using a differential equation to model restricted growth
using Euler's Method to find points on solution curves
6
The function, y=[x], has a ________ at every integer, since the left- and right-hand limits exist but are different.
removable discontinuity
squeeze continuity
jump discontinuity
infinite discontinuity
7
If a first-order differential equation in x and y is separable, how can that d.e. be written?
Both sides of the equation have x- and y-terms.
The equation has sinx on one side and cosx on the other.
All y-terms are on one side of the equation. All x-terms are on the other.
Neither side of the equation has x- or y-terms.
8
If the function y=f(x) is integrable on the interval a\le x\le b, then \frac{1}{b-a}\int_a^bf(x)dx=
the average value of f from a to b
the natural logarithms of f from a to b
the limits of f from a to b
the zeros of f from a to b
9
If f'(1)=0, or if f'(1) is undefined, then 1 is a ________ of f.
critical point
composite
remainder
central angle
10
Which of these functions is NOT continuous at each real number in its domain?
the trigonometric function, y = sinx
a polynomial function that has a degree of 4
an exponential function with a constant of 2
a rational function at a value that makes the denominator equal to 0
11
All of the following formulas can be used to find derivatives EXCEPT
the Power Rule
the One-to-One Rule
the Quotient Rule
the Product Rule
12
f'(x),y',and \frac{dy}{dx}are all ways of denoting the ________ of the function y=f(x).
amplitude
limit
derivative
period
13
L'Hospital's Rule can be applied to find the limit of an indeterminate form of the type _____.
x+0
\frac{0}{0}
\ln(e)
\frac{10}{1}
14
Which of the following is NOT true of the second derivative of a function?
It can be denoted as f''(x), \frac{d^2y}{dx^2}, or y''.
It is the (first) derivative of f'(x).
It can tell you whether the graph of a function is concave up or down.
It helps you calculate the area under a function.
15
The expression \int_{ }^{ }f(x)dx,which equals F(x)+C, is the __________ of the function f(x).
horizontal asymptote
infinite discontinuity
indefinite integral
corner

AP Calculus AB Flashcards | StudBud

AP Calculus AB

15 termsStudBud Administration948 plays

Flashcards15 cardsFPractice quizPHost liveL

Questions 15

Answers

1
Particle P moves along a line according to s=f(t). If s is the position of P on the line at time t, which is true?
The acceleration a of P at time t is given by \frac{ds}{dt}.
The velocity v of P at time t is given by \frac{ds}{dt}.
The velocity v of P at time t is given by \frac{dv}{dt}.
The speed of the particle is 2v.
2
If f is continuous on a closed interval [a,b] and F'=f, what is true according to the Fundamental Theorem of Calculus?
f'(c)=\frac{f(a+b)-f(a)}{b}
(f\circ a)(b)=f(a(b))
\int_a^bf(x)dx=F(b)-F(a)
\frac{f(b)-f(a)}{b-a}=f'(c)
3
Which theorem relates average rate of change and instantaneous rate of change and has Rolle's Theorem as a special case?
Extreme Value Theorem
Sandwich Theorem
Mean Value Theorem
Intermediate Value Theorem
4
If the region bounded by y=x^2,x=2,and y=0 is rotated about x=2, this finds the volume of the solid generated.
symmetry method
cross section method
disk method
general solution method
5
If you find the derivative of the outside function and then multiply by the derivative of the inside one, you are ____.
using the Chain Rule to differentiate a composite function
making a mistake in your calculations
using a differential equation to model restricted growth
using Euler's Method to find points on solution curves
6
The function, y=[x], has a ________ at every integer, since the left- and right-hand limits exist but are different.
removable discontinuity
squeeze continuity
jump discontinuity
infinite discontinuity
7
If a first-order differential equation in x and y is separable, how can that d.e. be written?
Both sides of the equation have x- and y-terms.
The equation has sinx on one side and cosx on the other.
All y-terms are on one side of the equation. All x-terms are on the other.
Neither side of the equation has x- or y-terms.
8
If the function y=f(x) is integrable on the interval a\le x\le b, then \frac{1}{b-a}\int_a^bf(x)dx=
the average value of f from a to b
the natural logarithms of f from a to b
the limits of f from a to b
the zeros of f from a to b
9
If f'(1)=0, or if f'(1) is undefined, then 1 is a ________ of f.
critical point
composite
remainder
central angle
10
Which of these functions is NOT continuous at each real number in its domain?
the trigonometric function, y = sinx
a polynomial function that has a degree of 4
an exponential function with a constant of 2
a rational function at a value that makes the denominator equal to 0
11
All of the following formulas can be used to find derivatives EXCEPT
the Power Rule
the One-to-One Rule
the Quotient Rule
the Product Rule
12
f'(x),y',and \frac{dy}{dx}are all ways of denoting the ________ of the function y=f(x).
amplitude
limit
derivative
period
13
L'Hospital's Rule can be applied to find the limit of an indeterminate form of the type _____.
x+0
\frac{0}{0}
\ln(e)
\frac{10}{1}
14
Which of the following is NOT true of the second derivative of a function?
It can be denoted as f''(x), \frac{d^2y}{dx^2}, or y''.
It is the (first) derivative of f'(x).
It can tell you whether the graph of a function is concave up or down.
It helps you calculate the area under a function.
15
The expression \int_{ }^{ }f(x)dx,which equals F(x)+C, is the __________ of the function f(x).
horizontal asymptote
infinite discontinuity
indefinite integral
corner