HSC Science (General) 12th Board ExamMaharashtra State Board
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# Solution - Discuss the continuity of the function f(x)=(1-sinx)/(pi/2-x)^2,= 3, for x=π/2 - HSC Science (General) 12th Board Exam - Mathematics and Statistics

#### Question

Discuss the continuity of the function

f(x)=(1-sinx)/(pi/2-x)^2,

= 3,                  for x=π/2

#### Solution

f(pi/2)=3 ......(given)

lim_(x->pi/2)f(x)=lim_(x->pi/2)(1-sinx)/(pi/2-x)

put pi/2-x=h then x=pi/2-h

As x->pi/2,h->0

lim_(h->0)(1-sin(pi/2-h))/h^2=lim_(h->0)(1-cosh)/h^2

=lim_(h->0)(1-cosh)/h^2xx(1+cosh)/(1+cosh)=lim_(h->0)(1-cos^2h)/(h^2(1+cosh))

=lim_(h->0)(sin^2h)/(h^2(1+cosh))=lim_(h->0)((sinh)/h)^2(1/(1+cosh))=1xx1/(1+1)

=lim_(x->pi/2)f(x)!=f(pi/2)

f(x) is discontinuous at x =pi/2

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#### APPEARS IN

Solution for question: Discuss the continuity of the function f(x)=(1-sinx)/(pi/2-x)^2,= 3, for x=π/2 concept: null - Discontinuity of a Function. For the courses HSC Science (General) , HSC Science (Electronics), HSC Science (Computer Science), HSC Arts
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