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प्रश्न
What is the values of' 'k' so that the function 'f' is continuous at the indicated point
पर्याय
4
6
8
10
MCQ
उत्तर
6
Explanation:
L.H.L = `lim_(h -> pi/2) (k cos x)/(pi - 2x)`, putting `x = pi/2 - h`
= `lim_(h -> 0) (k cos (pi/2 - h))/(pi - 2(pi/2 - h))`
= `lim_(x -> (pi^+)/2) (k cos x)/(pi - 2x)`,
R.H.L = `lim_(x -> (pi^+)/2) (k cos x)/(pi - 2x)`, putting `x = pi/2 + h`
= `k cos ((pi/2 + h))/(pi - 2(pi/2 + h))`
= `lim_(h -> 0) (- k sin h)/(-2 h)`
= `lim_(h -> 0) k/2 sinh/h = k/2`
`f(pi/2)` = 3 ......[Given]
`f` is continuous, if `k/2` = 3 or k = 6.
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