AP Calculus AB: Practice Final Exam
This set of flashcards focuses on understanding limits from graphs, the concept of average and instantaneous rates of change, and finding derivatives using basic rules and the chain rule. It also addresses common misconceptions about derivatives and tangent lines in calculus.
What is the limit of the function in the graph at x = 4?
2
Key Terms
What is the limit of the function in the graph at x = 4?
2
Evaluate the following as true or false. The average rate of change of a function f(x) between x=x1 and x=x2 is the slope of the line connecting the two points (x1,f(x1)) and (x2,f(x2)), and the derivative of the function f(x) at x is the slope of the line connecting the origin (0,0) and the point (x,f(x)).
false
Consider the function y = x^ 2 + x + 9. What is the equation of the tangent line at x = 2?
y=5x+5
Evaluate the following as true or false.The function f(x)=5 can be written as f(x)=5^1. Therefore, f′(x)=1⋅5^1−1
=1⋅5^0
=1⋅1
=1.
false
Find the derivative of:
v(x)=√(x+2)/^3√(x−3)
v′(x)=(x−13)/6(x−3)^4/3(x+2)^1/2
What is the derivative of the function
f(x) = cos^3(x^2−x)?
-3(2x−1)cos^2(x^2−x)sin(x^2−x)
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| Term | Definition |
|---|---|
What is the limit of the function in the graph at x = 4? | 2 |
Evaluate the following as true or false. The average rate of change of a function f(x) between x=x1 and x=x2 is the slope of the line connecting the two points (x1,f(x1)) and (x2,f(x2)), and the derivative of the function f(x) at x is the slope of the line connecting the origin (0,0) and the point (x,f(x)). | false |
Consider the function y = x^ 2 + x + 9. What is the equation of the tangent line at x = 2? | y=5x+5 |
Evaluate the following as true or false.The function f(x)=5 can be written as f(x)=5^1. Therefore, f′(x)=1⋅5^1−1 | false |
Find the derivative of: v(x)=√(x+2)/^3√(x−3) | v′(x)=(x−13)/6(x−3)^4/3(x+2)^1/2 |
What is the derivative of the function f(x) = cos^3(x^2−x)? | -3(2x−1)cos^2(x^2−x)sin(x^2−x) |
Find the derivative of A(x)=4e^[(cos4x)(sin3x)] | A’(x)=4e^[(cos4x)(sin3x)]⋅[3cos4xcos3x−4sin4xsin3x] |
Find f′(x) if f(x)=cos(2x^2) | f′(x)=−4xsin(2x^2) |
Use implicit differentiation to find an equation of the line tangent to the curve x ^2 + y ^2 = 10 at the point (3, 1). | y = −3x + 10 |
What is the inverse of f(x)=^3√1+x/2x? | f^−1(x)=1/2x^3−1 |
Which of the following is an antiderivative of arccsin x ? | xarcsinx+√1−x^2 |
A particle moves along the x-axis, with its position x given by x (t) = t − cos t. At which of the following times is the velocity of the particle equal to 0? | 3π/2 |
Which of the following is the second derivative off(x)=x^2−4/3x−6? | 0 |
A manufacturer wants to make open tin boxes from pieces of tin with dimensions 8 in. by 15 in. by cutting equal squares from the four corners and turning up the sides. Find the side of the square cutout that gives the box the largest possible volume. | 5/3 in. |
A television camera at ground level is filming at the lift-off of a space shuttle that is rising vertically according to the position equation | 2/29 rad/sec |
What are the critical points of the function f(x)=√x^2+1 ? | x = 0 |
On which of the following intervals is the graph of f(x)=x^2−1/2x+1 concave up? | (−∞,−1/2) |
Which of the following equations has no horizontal asymptote? | y=x^2−4/x |
Evaluate the indefinite integral∫⎛⎜⎝x^2+2x+1/x+1⎞⎟⎠dx. | x^2/2+x+C |
Evaluate the indefinite integral ∫t^2√t^3+1dt | 2/9(t^3+1)^3/2+C |
Evaluate ∫cosxsin^5xdx . | sin^6x/6+C |
What is the area bound by the curve h(x)=2πe4x+3x and the x-axis from x=0to x=2? | π/2e^8+6−π/2 |
Suppose you put a baseball machine at ground level, point it straight up, and fire a baseball into the air at 96 ft / s. How far has the baseball traveled after 5 s? | 208 ft |
What is the area of the region enclosed by y=x^2 and y=|x|? | 1/3 |
What is the area between the curves y=−x^2+4 and y=−3 ? | 28√7/3 |
What is the volume of the solid of revolution obtained by rotating the region bounded by y=2x^2+1,x=1, and x=0 around the x-axis? | 47π/15 |
The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take for a sample of 9 grams to decay to 0.72 grams? | 109.3 seconds |
When a particle is located at a distance x ft from the origin, a force of 3x^ 2 − 2x + 10 pound acts on it. How much work is done in moving it from x = 1 to x = 5? | 140 ft-lb |
Evaluate lim x→0√x+1/ln(x+1). | The limit does not exist. |
Compute dy/dx for y=(3^x2−x)^2/3−x^2 | 2(3x^2−x)(6x−1)(3−x^2)+2x(3x^2−x)2/(3−x^2)^2 |