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Let the equation of a curve be `x=a(theta+sin theta),y=a(1-cos theta)`. If `theta` changes at a constant rate k then the rate of change of the slope of the tangent to the curve at `theta=pi/3` is(a) `(2k)/sqrt3`(b) `k/sqrt3`(c) k(d) none of theseA. `2k//sqrt3`B. `k//sqrt3`C. kD. none of these |
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Answer» Correct Answer - D `(dy)/(dx)=((dy)/(d theta))/((dx)/(d theta))=(1)/(2)sec^(2).(theta)/(2).(d theta)/(dt)=(k)/(2)sec^(2).(theta)/(2)` `therefore" Required rate"=(k)/(2).sec^(2).(pi)/(6)=(k)/(2).((2)/(sqrt3))^(2)` |
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