InterviewSolution
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InterviewSolution
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If x=a (cos t + t sin t) and y=a ( sin t- t cos t), find `(d^(2)y)/(dx^(2))` |
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Answer» It is given that x =a (cos t + t sin t) and y=a (sin t - t cos t). Therefore, `(dx)/(dt)=a[-sin t+ sin t + t cos t]= at cos t` `(dy)/(dt)=a [ cos t -{cos t - t sin t} ] = at sin t` `therefore" "(dy)/(dx)=(((dy)/(dt)))/(((dx)/(dt)))=(at sin t)/(at cos t)= tan t` `"Then, "(d^(2)y)/(dx^(2))=(d)/(dx)((dy)/(dx))=(d)/(dx)(tan t)` `=(d)/(dt) (tan t)(dt)/(dx)` `=sec^(2) t. (dt)/(dx)` `sec^(2)t. (1)/(at cos t)` `(sec^(3) t)/(at)` |
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