HSC Science (General) 12th Board ExamMaharashtra State Board
Share
Notifications

View all notifications

If f(x) =(e^(x^2)-cosx)/x^2, for x= 0, is continuous at x = 0, find f(0). - HSC Science (General) 12th Board Exam - Mathematics and Statistics

Login
Create free account


      Forgot password?

Question

If `f(x) =(e^(x^2)-cosx)/x^2`, for x= 0, is continuous at x = 0, find f(0).

Solution

f(x) is continuous at x = 0

`lim_(x->0)f(x)=f(0)`

`f(0)=lim_(x->0)f(x)=lim_(x->0)(e^(x^2)-cosx)/x^2=lim_(x->0)((e^(x^2)-1)+(1-cosx))/x^2`

`=lim_(x->0)((e^(x^2)-1)/x^2+(1-cosx)/x^2)`

`=lim_(x->0)((e^(x^2)-1)/x^2+(2sin^2(x/2))/x^2)`

`=lim_(x->0)((e^(x^2)-1)/x^2+2(sin(x/2)/x)^2)`

`=lim_(x->0)((e^(x^2)-1)/x^2+2(sin(x/2)/(x/2)xx1/2)^2)`

`=lim_(x->0)(e^(x^2)-1)/x^2+1/2(lim_(x->0)sin(x/2)/x)^2`

`=1+1/2(1)^2`

`=3/2`

Thus,f(0)=3/2

  Is there an error in this question or solution?

APPEARS IN

 2016-2017 (March) (with solutions)
Question 5.1.3 | 3.00 marks
Solution If f(x) =(e^(x^2)-cosx)/x^2, for x= 0, is continuous at x = 0, find f(0). Concept: Continuity - Continuity of a Function at a Point.
S
View in app×