Thank you for registering.

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

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

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

⇐ BackProceed to Checkout ⇒
There are no items in this cart.
Continue Shopping
Book a free demo of live class

L’ Hospital’s Rule

 

We have dealt with problems which had indeterminate from either 0/0 or ∞/∞ .

The other indeterminate forms are ∞-∞,0,∞,00,∞0,1∞

We state below a rule, called L' Hospital's Rule, meant for problems on limit of the form 0/0 or ∞/∞  .

Let f(x) and g(x) be functions differentiable in the neighbourhood of the point a, except may be at the point a itself. If  limx→a f(x) = 0 = limx→a g(x) or limx→af(x)= ∞ = ∞  g(x), then limx→a f(x)/g(x) = limx→a f' (x)/g(x) = limx→a f' (x)/g'(x)    provided that the limit on the right either exists as a finite number or is ± ∞ .

Illustration:

Evaluate  limx→1 (1-x+lnx)/(1+cos π x )

Solution:

  limx→1 (1-x+lnx)/(1+cos π x ) (of the form 0/0)

= limx→1 (1-1/x)/(-π sin π  x) (still of the form 0/0)

=  limx→1 (x-1)/(πx sin π x) (algebraic simplification)

=  limx→1 1/(πx sin π x + π2 x cos π x ) (L' Hospital's rule again)

 = - 1/π2

Illustration:     

Evaluate limx→y  (xy-yx)/(xx-yy )

Solution:            

 limx→y  (xy-yx)/(xx-yy );   [0/0] = limx→y (yxy-1 - yx log y)/(xx log(ex) )

                                                     = (1-log y)/log(ey)
To read more, Buy study materials of Limtis and Continuity comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.


TOP Your EXAMS!

Upto 50% Scholarship on Live Classes

Course Features

  • Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution

Book a Live class Live courses Ask question