# Review of Calculus AB

### Review Test

Compute .

Compute .

What type of function is f (x) = x 6 ?

What type of function is f (x) = x 3 + 3x ?

What type of function is f (x) = x ?

For the following function, what value must be assigned to f (3) to make the function continuous at x = 3 ?

 f (x) =

A general expression for the derivative of f (x) is:

What is the derivative of f (x) = Π 4 ?

What is the derivative of f (x) = sin ?

What is the derivative of f (x) = ?

For the function f (x) = x 2 - 4x + 5 , give the equation of the tangent at x = 3 .

Find the equation of the line normal to the tangent of f (x) = x 2 - 4x + 5 at x = 1 .

Compute where x = 4x 2 y - 2y .

Car A and Car B start at the same point. At time t = 0 , Car A travels south at 40 miles per hour. Car B travels west at 20 miles per hour. At what rate is the distance between the two cars changing at t = 3 hours?

The momentum of an object is given by the relation p = mv , where m =mass and v =velocity. If an object weighing 3 kg accelerates at 2 m/s 2 , what is the rate of change of its momentum?

The position of an object is represented by s(t) = t 2 - t - 1 . What is the object's velocity at t = 3 seconds?

If the position of an object is represented by the equation s(t) = t 2 - t - 1 , what is the total distance traveled between t = 0 and t = 2 ?

Find a number c on [a, b] such that f'(c) = where f (x) = 2x 2 and [a, b] = [- 1, 2]

For the function f (x) = x 3 , is the critical point at x = 0 a local maximum, local minimum or neither?

Find the inflection points on the interval [- ,] for the function f (x) = sin(x) .

Does f (x) = have a horizontal asymptote?

Sophia is standing 1000 feet away from the base of a tall building. At time t = 0 , she sees a baby drop from the roof of that building and calculates that it will hit the ground in 21 seconds. Her normal running speed is 10 feet per second, but she can increase her speed by 10 feet per second with each apple she eats. If it takes her one second to eat an apple, how many apples should she eat in order to minimize the total time it will take (eating + running) to get to the base of the building?

A triangle has two sides that are each 5 cm long. What angle between the two sides will maximize the triangle's area?

Let F(x) = x 4 - 2x . What kind of point occurs at x = 3 ?

What is the derivative of f (x) = ?

Evaluate 7dx .

Evaluate sin(7x+17)dx .

Evaluate cos(Π-x)dx.

Evaluate t dt

Using left endpoints and 4 rectangles, approximate x 2 dx .

Using right endpoints and 4 rectangles, approximate x 2 dx .

Evaluate x 2sin dx .

Evaluate sin(x)dx .

The velocity of a particle is given by the equation v(t) = t 3 - 2 . What is the total change in position from t = 0 to t = 2 ?

What is the average value of f (x) = 11x 2 - 2 on [-1,1]?

What is the average value of f (x) = on [0, 2Π] ?

Compute sin(t 4)dt .

Evaluate cos(t+4)dt .

Using 4 trapezoids, approximate x 2 dx .

If f (x) = x 3 , compute f -1 (2) .

Evaluate Π x .

Evaluate x Π .

Evaluate x x .

What is the rate constant of a substance that decays 27\% after 20 minutes?

If = 7y , what is a possible equation for the corresponding function?

Evaluate log3387 .

Evaluate dx .

Evaluate e 3x dx .

Evaluate log7(56) - log7(8) .

Evaluate 7x dx .

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