HSC Arts 12th Board ExamMaharashtra State Board
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If the function f (x) is continuous in the interval [-2, 2],find the values of a and b where - HSC Arts 12th Board Exam - Mathematics and Statistics

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Question

If the function f (x) is continuous in the interval [-2, 2],find the values of a and b where

`f(x)=(sinax)/x-2, for-2<=x<=0`

`=2x+1, for 0<=x<=1`

`=2bsqrt(x^2+3)-1, for 1<x<=2`

Solution

Since the function f (x) is continuous in the interval [-2,2]

 f is continuous at in x = 0 and x = 1
(i) continuity at x = 0

`lim_(x->0)f(x)=lim_(x->0)((sinax)/x-2)`

`=lim_(x->0)((sinax)/(ax)a-2)`

=a(1)-2

=a-2

f (x)= 2x +1, for 0<= x <=1 ...(i)
f(0)=2(0)+1=1

f is continuous at x=0

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

a-2=1

a=3

(ii) Continuity at x = 1

From (i), f(1)=3

`lim_(x->1)f(x)=lim_(x->1^+)(2bsqrt(x^2+3)-1)`

`=2blim_(x->1)sqrt(x^2+3)-1`

`=2bsqrt(1+3)-1=4b-1`

f is continuous at x = 1

`lim_(x->1)f(x)=f(1)`

4b-1=3

4b=4

b=1

  Is there an error in this question or solution?

APPEARS IN

 2013-2014 (March) (with solutions)
Question 5.2.3 | 4.00 marks
Solution If the function f (x) is continuous in the interval [-2, 2],find the values of a and b where Concept: Continuity - Continuity in Interval - Definition.
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