Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

please explain the wavy curve method and la hospital rule with examples

please explain the wavy curve method and la hospital rule with examples

Grade:11

1 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
10 years ago

Dear Abhik

Wavy curve method :--

 

1 . put only odd power factors in numerator and denominator  equal to zero separately as function changes sign only for odd power

2.  Plot these points  on the number line in increasing order  .

3. Now check the coefficients of X and make them positive.

4. expression will be +ve to the right of the highest point allotted on number line.

5.  alternately assign + and - signs in rest of intervals ( from right to left )

 

to see examples see the pic

 

L'Hôpital's rule

l'Hôpital's rule states that for functions ƒ and g:

If \lim_{x \to c}f(x)=\lim_{x \to c}g(x)=0 \, or \pm\infty and \lim_{x\to c}f'(x)/g'(x) exists,

then \lim_{x\to c}\frac{f(x)}{g(x)} = \lim_{x\to c}\frac{f'(x)}{g'(x)}.

Here is  example involving 0/0:

\lim_{x\to 0}{\frac{e^x-1-x}{x^2}} =\lim_{x\to 0}{\frac{e^x-1}{2x}} =\lim_{x\to 0}{\frac{e^x}{2}}={\frac{1}{2}}.

Here is another example involving ∞/∞:



\lim_{x\to 0^+} x \ln x =\lim_{x\to 0^+}{\frac{\ln x}{1/x}} =\lim_{x\to 0^+}{\frac{1/x}{-1/x^2}} =\lim_{x\to 0^+} -x = 0.

 

All the best.

AKASH GOYAL

AskiitiansExpert-IITD

 

Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..

 


301_23499_Photo-01101.jpg

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free