Cracking The Ap Calculus ab Exam 2018

. Let’s use trigonometric identities to simplify the limit: = = = . Now, if we tak ...

10. 1 Recall L’Hôpital’s Rule: If f(c) = g(c) = 0, or if f(c) = g(c) = ∞, and if f′(c) and g′(c) ...

take the derivative: = − 3 − 2x. Now, we can find the slope, m: = − 3 − 3(0) = − 3. F ...

answer is only . It’s very important to check that the answers you get for c fall in the given inte ...

Thus, in order to find the maximum profit, we need to plug all four values of x into the profit equat ...

First, let’s draw a picture of the situation. We will draw a circle of radius 10 centered at the or ...

Note that the figure is symmetric above and below the x-axis, so we could maximize the area above the x-a ...

Move the right-hand term to the other side of the equals sign: Cross-multiply: 2(100 − x^2 ) = 2x^2 Di ...

, then y = . So there are points of inflection at and . Next, we need to determine if each ...

Maximum at (0, 0); Vertical asymptotes at x = 2 and x = −2; Horizontal asymptote at y = 3; No point ...

(0, 0). Note also that the function is positive for x < 0 and negative for x > 0, so the cu ...

3 m/s We are given the rate at which the volume of the fluid is increasing, = 108π, and are looking fo ...

function: = = . Next, we set the velocity equal to zero. The solutions are: t = ±3. We can i ...

f′(x) = ln (cos 3x) − 3x tan 3x −3x^2 The rule for finding the derivative of y = ln u is , where ...

Rule to find the derivative: f′(x) = (ln x) + (log x) . This can be simplified to f′ (x) = . f′ ...

is very difficult to solve for the inverse value of y. If the algebra looks difficult, look for an obvious s ...

If we take the limit as x goes to 0, we get an indeterminate form , so let’s use L’Hôpital’s Rule. ...

x^5 − x^3 + x^2 + 6x + C Here we will use the Power Rule, which says that . The integral ...

Here we will use the Power Rule, which says that . First, let’s simplify the integrand: = ...

and ∫cos x dx = sin x + C. First, we need to rewrite the integrand, using trig identities: ...