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If the function f(x) = {((sin^(2)ax)/(x^...

If the function `f(x) = {((sin^(2)ax)/(x^(2))","," when "x != 0),(" k,"," when " x = 0):}`is continuous at x = 0 then k = ?

A

3

B

`-3`

C

`-5`

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
`f((pi)/(2) - 0) = underset(h rarr 0)(lim) (k cos ((pi)/(2) - h))/(pi -2((pi)/(2) - h)) = underset(h rarr 0)(lim) (k sin h)/(2h) = (k)/(2) underset(h rarr 0)(lim) (sin h)/(h) = ((k)/(2) xx 1) = (k)/(2)`
`f((pi)/(2) + 0) = underset(h rarr 0)(lim) (k cos ((pi)/(2) + h))/(pi -2((pi)/(2) + h)) = underset(h rarr 0)(lim) (-k sin h)/(-2h) = (k)/(2) underset(h rarr 0)(lim) (sin h)/(h) = (k)/(2)`
`:. (k)/(2) = 3 rArr k = 6`
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