Calc problem?

Question

If someone could explain how this is done, I would really appreciate it.

Find the following limits using L'Hopital's Rule whenever it applies.

a) limit as x approaches 0 of cos squared x divided by x
b) limit as x approaches 0^+ of square root of x times ln(x)
c) limit as x approaches infinity of x/(e^x)

Answer 1

a) (cos^2 x)/x ... top is bounded, x-->0 so expr -->oo
b) sqrt(xln(x)) ..
for 0 consider x = 1/e^n : x ln(x) = -n/e^n -->0 as n-->oo
expr = i sqrt(x(-ln(x) )) -->0i
c) x/e^x --> 1/e^x [l;hopital] -->0

Answer 2

a) 0/0

lim 2 cosx(- sinx)/1
=2 cos0 (-sin0)/1
=2 * 1 * 0
=0

c)
infinity/infinity

lim 1/e^x
=1/infinity
=0