Cracking The Ap Calculus ab Exam 2018

2. The area is (3)(2) = 3. Thus, the value of the integral is 7 − 3 = 4.


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

Rule.    We  take    the     derivative  of  the     numerator   and     the     denominator     and     we  get    

. When we take the limit, we again get an indeterminate form ,

so  let’s   use L’Hôpital’s Rule    a   second  time.   We  take    the derivative  of  the numerator   and the

denominator  and     we  get     .   Now,    when    we  take    the     limit,  we  get    

    =   0.

7. C Here we need to use the Product Rule, which is: If f (x) = uv, where u and v are both functions

of  x,  then    f′(x)   =   .

We  get f′(x)   =       +   .

This    can be  simplified  to.

Multiply     the     numerator   and     denominator     of  the     second  expression  by  to  get     a

common  denominator :       +   .

This     simplifies  to  =   =  

.

8. C We find the instantaneous rate of change of the function by taking the derivative and plugging in
   t = −1.

We  need    to  use the Quotient    Rule,   which   is