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
Dear ajit pal
y= Lt x→o xx
log y = Lt x→o xlog x
=Lt x→o (log x)/(1/x)
=Lt x→o (1/ x)/(-1/x2)
=Lt x→o (- x)
=0
y=e0
y=1
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin
lim x^x x -> 0 I'm not sure this limit exists unless the limit is one-sided. I'll assume it to be one-sided. lim x^x x -> 0+ Use the property y = e^(ln(y)). Since e and natural log are inverses of each other, they cancel each other out. lim e^(ln(x^x)) x -> 0+ Use the log property to move the x outside of the log. lim e^[x ln(x)] x -> 0+ Move the limit inside of the exponent. e^[ lim (x ln(x)) ] . . x -> 0+ Now the limit is of the form [0*infinity], which is indeterminate. Let's move x to the denominator as (1/x). e^[ lim ( ln(x)/(1/x) ) ]
. . x -> 0+ How the form is [infinity/infinity]. Use L'Hospital's rule. The derivative of ln(x) is (1/x). The derivative of (1/x) is (-1/x^2). e^[ lim ( (1/x)/(-1/x^2) ) ] . . x -> 0+ Simplify. e^[ lim ( (-x^2)/x ] . . x -> 0+ e^[ lim (-x ) ]. . x -> 0+ And evaluate the limit e^0 Which is just 1
--
regards
Ramesh
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
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !