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If x=acos^3theta,y=bsin^3theta ,fin d (d...

If `x=acos^3theta,y=bsin^3theta` ,fin d `(d^3y)/(dx^3)` at `theta=0.`

Text Solution

Verified by Experts

The correct Answer is:
Does not exist
`x=acos^(3) theta, y = b sin^(3)theta`
`y_(1)=(dy)/(dx)=(3b sin^(2) theta cos theta)/(-3a cos^(2) theta sin theta)`
`=-(b)/(a) tan theta, if sin theta ne 0, cos theta ne 0`
Therefore, `y_(1)` does not exist a `theta = 0.`
Hence, `y_(2) and y_(3)` do not exist at `theta=0.`
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