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Find the equation of tangent to y=int(x...

Find the equation of tangent to `y=int_(x^2)^(x^3)(dt)/(sqrt(1+t^2))a tx=1.`

Text Solution

Verified by Experts

The correct Answer is:
`sqrt(2)y=x=1`
`y|_(x=1)=0,(dy)/(dx)=1/(sqrt(1+x^(5))) 3x^(2)-1/(sqrt(1+x^(4)))2x`
or `(dy)/(dx)|_(x=1)=1/(sqrt(2))`
Thus, required equation is `ysqrt(2)=x-1`.
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