Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
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
Evaluate limx→y (xy-yx)/(xx-yy )
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.
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Second Order Derivative Table of Content First...
Limits, Continuity & Differentiability –...
Exponential and Logarithmic Functions Table of...
Continuity Table of Content Introduction to...
General Theorems on Differentiation General...
Continuity in Interval Table of Content...
Limits using Sandwich Theorem and...
Limits Table of Content Limits Graphical...
Limits & Continuity Table of Content Limit of...
Differentiability Table of Content...
Discontinuity Table of Content Important Points...
Algebra of Limit Table of Content Can a function...
Limits Left and Right Limit Let y = f(x) be a...