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

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

 

 

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APPEARS IN

 2014-2015 (March) (with solutions)
Question 6.1.1 | 3 marks
 2015-2016 (July) (with solutions)
Question 6.1.3 | 3 marks
Solution for question: Find a and b, so that the function f(x) defined by concept: null - Continuity of a Function at a Point. For the courses HSC Science (Electronics), HSC Science (General) , HSC Science (Computer Science), HSC Arts
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