Question

5) Apply the L'Hospital's Rule to find each limit: 2x – 1 – 2x - 2x² a) lim,70- b)lim. Va Inx

Answer 1

073

(0/0 form applying L'hospital rule)

= lim 10 (e2r -1 -2.-2.) (23)

= lim 2e21 – 0 -2 -2 * 22 3.72 10
(Because
2 dr(e) =
,
do(') = n2-1
)

2es - 2 - 4.1 = lim - 1-0 32

(0/0 form again applying L'hospital rule)

= lim 10 (2e27 – 2 - 4x) (3.12)

= 2*2e2r - 0-4 lim - 103* 21

4e2x - 4 = W 19

(0/0 form again applying L'hospital rule)

= lim dr (4e21 – 4) (6.) 1+0

4* 2er - 0 = lim - 6

8e27 = lim 0 - 6

/

$=\frac{8}{6}$

$\boldsymbol{=\frac{4}{3}}$

--------------------------------

lim Ve In r0+

In (2) = lim 10+

(infinity/infinity form applying L'hospital rule)

= lim 1+0+ din () Go

= lim In (1) (-1/2) 10+

= lim 10+ 2r3/2
(Because
(In x) = ?
and
do(') = n2-1
)

= lim (-2.1/2) 10+

= -270) 1/2

$=0$