Join now for JEE/NEET and also prepare for Boards Class 10 Boards Cancelled! What to do next ? Ask our Experts in a Free Counseling Session Now ! Register Now
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
1800-1023-196
+91 7353221155
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
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
Illustration 1: Let [.] denotes the greatest integer function and f(x) = [tan2x], then does the limit exist or is the function differentiable or continuous at 0? (1999)
Solution: Given f(x) = [tan2x]
Now, -45°< x < 45°
tan(-45°)< tanx < tan45°
-tan 45°< tan x < tan 45°
-1< tan x <1
So, 0 <tan2x < 1
[tan2x] = 0
So, f(x) is zero for all values of x form x = -45° to 45°.
Hence, f is continuous at x =0 and f is also differentiable at 0 and has a value zero.
Illustration 2: A function is defined as follows:
f(x)= x3 , x2< 1
x , x2≥ 1
Discuss the differentiability of the function at x=1.
Solution:We have R.H.D. = Rf'(1)
= limh→0 (f(1-h)-f(1))/h
= limh→0 (1+h-1)/h = 1
and L.H.D. = Lf'(1)= limh→0 (f(1-h)-f(1))/(-h)
= limh→0 ((1-h)3-1)/(-h)
= limh→0 (3-3h+h2) = 3
?Rf'(1)≠ Lf'(1)⇒ f(x) is not differentiable at x=1.
Illustration 3:If y = (sin-1x)2 + k sin-1x, show that (1-x2) (d2 y)/dx2 - x dy/dx = 2
Solution: Here y = (sin-1x)2 + k sin-1x.
Differentiating both sides with respect to x, we have
dy/dx = 2(sin-1 x)/√(1-x2 ) + k/√(1-x2 )
⇒(1-x2 ) (dy/dx)2 = 4y + k2
Differentiating this with respect to x, we get
(1-x2) 2 dy/dx.(d2 y)/(dx2 ) - 2x (dy/dx)2 = 4(dy/dx)
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