Question

L Hopital

I have to solve this: http://screencast.com/t/AY0m9I2Ds


What exactly is the L Hopital rule ?

Answer 1

on the first one, write tan using sin and cos to get rid of the bad spot.
for the second one, factor top and bottom and cancel common factors

Answer 2

L'Hopital's Rule see 2nd page

Answer 3

Can you tell me how will I check the answer of the first question with L hopital rule ? If I understand the first one I will do the others

Answer 4

so the first is this
\[\lim_{x \rightarrow 0}\frac{ \sin x }{ \tan x }=\frac{ 0 }{ 0 }\Rightarrow \lim_{x \rightarrow 0}\frac{ \sin x }{ \tan x }=\lim_{x \rightarrow 0}\frac{ \cos x }{ \sec^2 x }=\lim_{x \rightarrow 0} \cos^3 x =1\]

Answer 5

Can you pelase explain me this step http://screencast.com/t/08uE0OHj4dF

Answer 6

how did you make cos^(3)x

Answer 7

Because secant is 1/cosine... try it on paper and you'll see why it becomes cos^3x

Answer 8

`Thanks !!

Answer 9

\[\lim_{x \rightarrow 0}\frac{ \sin x }{ \tan x }\overset {H}{=}\lim_{x \rightarrow 0}\frac{ \cos x }{ \sec^2 x }=\]

Answer 10

L'hopitals rule is basically: differentiate the numerator, and differentiate the denominator

But it's only valid for indeterminate forms, like 0/0, inf/inf, etc