Cracking The Ap Calculus ab Exam 2018

100 km/hr We are given the rate at which Car A is moving south, = 80, and the rate at which Car B ...

− in./s. We are given the rate at which the water is flowing out of the container, = − 35π (Why ...

The vertical distance from the dock to the bow is always 7, so, using the Pythagorean Theorem, we get: 7^2 ...

24 y = 6x + 6y 3 y = x Next, we take the derivative of the equation with respect to t: 3 = . ...

Note that the radius is 6 (the length of the minute hand) and is a constant. Next, we take the deri ...

< 3π, and 3π < t < 4±. When 0 < t < π, the velocity is positive, so the particle i ...

Therefore, the particle travels a distance of 48. Velocity is 0; acceleration is 0. This should not be a ...

f′(x) = The rule for finding the derivative of y = ln u is , where u is a function of x. Here ...

0 + 2 = . f′(x) = ex cos x (cos x − x sin x) The rule for finding the derivative of y = eu ...

derivative of y = eu is = eu , where u is a function of x. Here we will use the Quotient Rul ...

The rule for finding the derivative of y = au is = au(ln a) , where u is a function of x. Here ...

3 x − 5x^3. With a little algebra, you should get x = −1. Or, if you are permitted, use your calculator. No ...

4. First, we take the derivative of y: = 1 + 3x^2 . Next, we find the value of x where y = − ...

plugging in the value of x that makes y equal to a: = = 1. 6. 1 First, we take the derivati ...

Recall the differential formula that we use for approximating the value of a function: f(x + ∆x) ≈ f(x) ...

that it has a radius of length 5 mm with an increase of 0.01 mm, where V(r) = πr^3 (the volu ...

SOLUTIONS TO PRACTICE PROBLEM SET 17 1. Recall L’Hôpital’s Rule: If f(c) = g(c) = 0, or if f(c) = g( ...

again! We take the derivative of the numerator and the denominator: . If we take the limit, we get . We ne ...

to get messier. Let’s try using trigonometric identities to simplify the limit. If we rewrite the numerator ...

infinitely often). 7. Recall L’Hôpital’s Rule: If f(c) = g(c) = 0, or if f(c) = g(c) = ∞, and if f ...