HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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# Find a and b, so that the function f(x) defined by - HSC Science (Electronics) 12th Board Exam - Mathematics and Statistics

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ConceptContinuity Continuity of a Function at a Point

#### Questions

Find a and b, so that the function f(x) defined by

f(x)=-2sin x,       for -π≤ x ≤ -π/2

=a sin x+b,  for -π/2≤ x ≤ π/2

=cos x,        for π/2≤ x ≤ π

is continuous on [- π, π]

Find α and β, so that the function f(x) defined by

f(x)=-2sin x,       for -π≤ x ≤ -π/2

=α sin x+β,  for -π/2≤ x ≤ π/2

=cos x,        for π/2≤ x ≤ π

is continuous on [- π, π]

#### Solution

f(x)=-2sinx, " for " -pi<=x<=-pi/2

=asinx+b , " for " -pi/2<x<pi/2

=cosx , " for " pi/2<=x<pi

f(x) is continuous for x=-π/2

RHL,

=lim_(x->-pi/2)asinx+b

=asin(-pi/2)+b

=-a+b

f(-pi/2)=-2sin(-pi/2)

therefore-a+b=2........(i) [because f(x) " is continuous for "x=-x/2]

f(x) " is continuous for "x=pi/2

LHL,

=lim_(x->pi/2)asinx+b

=asin(pi/2)+b

=a+b

f(pi/2)=cos(pi/2)=0

a+b=0   .........(ii)

Solving (i) and (ii)

a= -1 and b=1

Is there an error in this question or solution?

#### APPEARS IN

2015-2016 (July) (with solutions)
Question 6.1.3 | 3.00 marks
2014-2015 (March) (with solutions)
Question 6.1.1 | 3.00 marks
Solution Find a and b, so that the function f(x) defined by Concept: Continuity - Continuity of a Function at a Point.
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