Click to Chat

1800-2000-838

+91-120-4616500

CART 0

• 0

MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 320 off
USE CODE: MOB20

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


6 years ago

Share

										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

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.


6 years ago

# Other Related Questions on Differential Calculus

Plz help me solve this question. It is from chapter limits and derivatives . I did not find that in the list,

Krishna, write your questions that you want to ask, to related to limits and derivative. But you studied the defnition of limits and derivative clearly.

 Kumar 4 months ago

Try desmos (Google it ) ... It is used to graph the function.. Then you can set y as a parameter and then you will see that the function as x-> 0 the graph tends to infinity (for some values...

 rishabh 3 months ago

Kumar the question is lim x--> 0 ((y^2 - (y-x)^2)^1/x). / (8xy - 4x^2 + (8xy)^1/2)^3 I have also attached the image of it with the question please take a look

 Sujith krishna 4 months ago
Why does lhl and rhl are not equal in this question.w hat should i do in these type of questions

coz this is not 0/0 inderminate form ...it is exact 0/0 which is not defined(n.d.)

 Nishant Vora one month ago

 Nishant Vora one month ago

Why cannot we write tan[x]/[x] as 1 when x tends towards zero..and if is in 0/0 form why didnt u used lhospital rule

 Samaksh one month ago
i can not solve this inequality please sir how to solve this inequality Ix+1I+Ix-2I

i am trying to write conditions in the answer but after posting the conditions are vanishing , you can see above, dont know why is it happening.... :(

 DR STRANGE 16 days ago

Ix+1I+Ix-2I = 2x-1 ….....for x>2 =x+1 -(x-2) = 3 …......for -1 = -(x+1) -(x-2) = 1-2x ….......for x

 DR STRANGE 16 days ago

mistake............................................................... =3 for...... -1 = 1-2x ….for x

 DR STRANGE 16 days ago
If alpha is a real root of the equation ax 2 +bx+c and beta is a real root of equation -ax 2 +bx+c. Show that there exists a root gama of the equation (a/2)x 2 +bx+c which lies between alpha...

 Ajay 6 months ago

Small Mistake in last para posting again..............................................................................................................

 Ajay 6 months ago

We have Similarly, So if P(x) = a/2 x 2 +bx +c, then and are off opposite sign and hence there must exist a root between the two numbers.

 mycroft holmes 6 months ago
In the listed image can you tell me how beta*gamma = 2 ….. . . .. ??

The value of gamma is still not correct, either printing mistake or you gave me wrong value. The correct value of gamma is below

 Ajay 5 months ago

Thankyou so much............................. …......................................................................!

 Anshuman Mohanty 5 months ago

Yes sorry..... . . . .it is not so clear.. ok the values are beta = α + α^2 + α^4 and gamma = α^3 + α^5 + α^7

 Anshuman Mohanty 5 months ago
if |z - i| Options: a*) 14 b) 2 c) 28 d) None of the above

If |z-i| = ?? PLs complete the question

 Nishant Vora one month ago

Got it! [z + 12 – 6 i ] can be rewritten as [ z – i + 12 – 5 i] => | z – i | and => |12 – 5 i | = sqrt ( 12^2 + 5^2) = 13......................(2) => | z + 12 – 6 i | => | z + 12 – 6 i |...

 Divya one month ago

I tried posting the question several times, it kept cutting off the rest of the question. Here: If | z-1| Options: a*) 14 b) 2 c) 28 d) None of the above

 Divya one month ago
View all Questions »

• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: R 15,000
• View Details
Get extra R 3,000 off
USE CODE: MOB20

Get extra R 320 off
USE CODE: MOB20

More Questions On Differential Calculus