Question

Explain L hospitals rule along with examples?plz do fast and give answer only if u know the exact answer...​

Answer 1

Answer:

L hobital rule is valid

in 0/0 or

infinite /infinite cases

in this rule

we have to generally differentiate the term

and we have to put the value in first derivative

For example Limx->0 sinx/1-cosx

general different.

=cosx/1+sinx

x=0

limit is 1/1-0

=1

ok

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Answer 2

Answer:

Example 1:

Evaluate limx→0 (2 sin x – sin 2x) / (x – sin x)

Solution:

Given:

limx→0 (2 sin x – sin 2x) / (x – sin x)

Differentiate the above form, we get

= limx→0 (2 cos x – 2 cos 2x) / (1 – cos x)

= limx→0 (-2 sin x + 4 sin 2x) / (sin x)

= limx→0 (-2 cos x + 8 cos 2x) / (cosx)

Now substitute the limit,

= -2+8/1 = 6/1 = 6

Therefore, limx→0 (2 sin x – sin 2x) / (x – sin x) = 6.