HSC Science (General) 12th Board ExamMaharashtra State Board
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# 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

ConceptContinuity Continuity of a Function at a Point

#### 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.
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