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If `x = sin theta, y = sin^(3) theta` then `(d^(2)y)/(dx^(2))` at `theta = (pi)/(2)` is …….A. 3B. 6C. `(1)/(6)`D. `(1)/(3)` |
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Answer» Correct Answer - B We have, `x = sin theta, y = "sin"^(3) theta` `:. (dy)/(dx) = ((dy)/(d theta))/((dx)/(d theta)) = (3"sin"^(2) theta(cos theta))/(cos theta)` `implies (dy)/(dx) = 3 "sin"^(2) theta` Now, `(d^(2)y)/(dx^(2)) = 3 (2 "sin" theta cos theta) (d theta)/(dx)` at `theta = (pi)/(2), (d^(2) y)/(dx^(2)) = 6 "sin" ((pi)/(2)) = 6 xx 1 = 6` |
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