Posted by angie on .
Find the following limits algebraically or explain why they don’t exist.
lim x>0 sin5x/2x
lim x>0 1cosx/x
lim x>7 x7/x7
lim x>7 (/x+2)3/x7
lim h>0 (2+h)^38/h
lim t>0 1/t  1/t^2+t

Calculus 
Reiny,
a lot of your questions contain ambiguous typing
e.g. the second last one probably says
lim ( (2+h)^3  8)/h as h > 0
You could expand the top, or recognize it as a difference of cubes
recall A^3  B^3 = (AB)(A^2 + AB + B^2)
= lim [(2+h  2)((2+h)^2 + 2(2+h) + 4) )/h , h>0
= lim (2+h)^2 + 2(2+h) + 4 , h> 0
= 4 + 4 + 4 = 12
for the first one
I will again assume you meant
lim sin (5x) / (2x) , as x > 0
recall that lim sinØ/Ø = 1 as Ø >0
so let's "construct" this pattern
multiply top and bottom by (5/2)
so
lim sin (5x) / (2x) , as x > 0
= lim (5/2)sin (5x)/( (2x)(5/2)
= (5/2) lim sin (5x) / (5x) , as x>0
= (5/2)(1) = 5/2
try some of the others now after checking on your typing using brackets.