Cracking The Ap Calculus ab Exam 2018

ANSWERS AND EXPLANATIONS TO SECTION I

1. B First, take the derivative.

g′(x)   =    (4x^3 )    −   5(2x)   =       −   10x

Now,    plug    in  4   for x.

− 10(4) = 8 − 40 = −32

2. 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:   

= −16.

3. B Notice that if we plug 5 into the expressions in the numerator and the denominator, we get ,

which   is  undefined.  Before  we  give    up, we  need    to  see if  we  can simplify    the limit   so  that    it

can be  evaluated.  If  we  factor  the expression  in  the numerator,  we  get  ,  which

can be  simplified  to  x   +   5.

Now,    if  we  take    the limit   (by plugging    in  5   for x), we  get 10.

4. D We need to use the Quotient Rule, which is

Given   f(x)    =    ,  then    f′(x)   =   .

Here    we  have