Cracking The Ap Calculus ab Exam 2018

Here,    we  can     rewrite     the     expression  as  =   =  .

Remember    Rule    No. 4,  which   says    that     .  Here,       =       =   

. If we want to evaluate the limit the long way, we first divide the numerator and the

denominator of  the expression  by  x:   .  Next,   we  multiply    the numerator   and the

denominator of  the top expression  by  7   and the numerator   and the denominator of  the bottom

expression  by  5.  We  get  .  Now,    we  can evaluate    the limit:      =   .

18. The limit Does Not Exist.

The value   of  sin x   oscillates  between −1  and 1.  Thus,   as  x   approaches  infinity,   sin x   does    not

approach    a   specific    value.  Therefore,  the limit   Does    Not Exist.

Here,   as  x   approaches  infinity,       approaches  0.  Thus,       sin     =   sin 0   =   0.

20.

We  can break   up  the limit   into     .  Remember    Rule    No. 4,  which   says    that    

    =    .  Here,       =       ×       =    .  If  we  want    to  evaluate    the limit

the  long    way,    we  first   divide  the     numerator   and     the     denominator     of  the    expressions  by x:  

. Next, we multiply the numerator and the denominator of the top expression

by   7   and     the     numerator   and     the     denominator     of  the     bottom  expression  by  11.     We  get    

. Now, we can evaluate the limit: =

= = .