Cracking The Ap Calculus ab Exam 2018

28. D Here, we use the Chain Rule.

Step    1:  First,  take    the derivative  of  the outside function.

The derivative  of  ln  u   is  .

We  get

    ln(ln(u))   =   

Step    2:  Now we  take    the derivative  of  the function    in  the denominator.    Once    again,  the function

is  ln  u.

We  get

29. C Note that if we plug in zero, we get a limit of the indeterminate form , so we can use

L’Hôpital’s Rule    to  find    the limit.  Take    the derivative  of  the numerator   and the denominator:    

. Now, if we plug in 0 we get: = − 1.
30. A We can do this integral with u-substitution.

Step    1:  Let u   =   tan x.  Then    du  =   sec^2 x dx.

Step 2: Substituting, we get ∫ tan^6 x sec^2 x dx = ∫ u^6 du.

Step 3: This is an easy integral: ∫ u^6 du = + C.