Question

How D.L.Hospital Rules Applies

Answer 1

If your numerator and denominator is in the form :

0/0 or infinity/infinity, then

Take the derivative for first time to see whether you are getting rid of 0/0 or infinity/infinity form..

Answer 2

For example:

\[\lim_{x \rightarrow 0} (\frac{\tan(x)}{x})\]

Answer 3

So here you are getting, 0/0 form when you put x = 0 here :

So: apply here L hospital rule..

Answer 4

plz explain me inn detial with example

Answer 5

I have given you example above..

Can you tell me what do you get there when you will directly put x = 0 there??

Answer 6

we got 0 up and down

Answer 7

Yep..

so to avoid this condition we will use L hospital Rule..

Okay??

Answer 8

Now take the derivative on up and down side with respect to x..

Can you do it, say yes or no directly..

Answer 9

thats why we take derivative up and down

Answer 10

tell me what is the derivative of tan(x) ??

Answer 11

1/cotx

Answer 12

Yes, this is the reason we are taking derivative up and down..

In case you get infinity/infinity, then also you will take derivative..

Okay??

Answer 13

ok

Answer 14

Dude, this is the other form of tan(x)..

I said to tell the derivative of tan(x)..

Have you studied derivatives or differentiation yet??

Answer 15

yes

Answer 16

Anyways,

\[\frac{d}{dx} \tan(x) = \sec^2(x)\]

Answer 17

ohhh yes yes

Answer 18

And tell me what is the derivative of x??

Answer 19

1

Answer 20

Yep..

So finally tell me now what is your limit has become after taking derivative??

Answer 21

\[\lim_{x \rightarrow 0} \frac{\sec^2(x)}{1}\]

Right ??

Answer 22

yes

Answer 23

And now put x = 0 here and tell me what did you get ??

Answer 24

\[\sec^2(0) = ??\]

Answer 25

we get 0

Answer 26

How ?

Answer 27

Do you know the value of :
\[\sec(0)\]

Answer 28

sorry we get 1 and divide by 1 so we get 1 ans

Answer 29

Yep...

So it is solved by using L hospital Rule..

Clear??

Answer 30

i mix sec with sin hahahaha

Answer 31

Ha ha ha...

Be careful next time..

Answer 32

yep but its difficult to solve long and lenthy questions

Answer 33

where you from r u a teacher ?

Answer 34

I am just a student like you.

Not a teacher..