A curve is given by the equation x4 + y = 82. Find the equation of the line tangent the curve at point (-3,1) by doing the following steps:

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A: This question can be solved using the concept of linear differential equation and limits.

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A: As per Bartleby guidelines rule I am answering only first question as second question is not a…

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A: To find out the integration.

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A: Solution of given question is written in below steps.

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A: Trigonometric Identity: sec2x=1+tan2x

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A: We use double angle formula  cos(2x) =2cos2(x)-1  cos2(x) =(1+cos(2x))/2

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A: Topic = Derivative

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A: Here we have to find the radius of the curvature of y=x4 at (1,1)

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A: I am attaching image so that you understand each and every step.

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A: Given  ∫2x2+x+1x-1x+1x-2dx = ∫Ax-1+Bx+1+Cx-2 dx

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A: use derivative for finding the instantaneous rate

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A: I am attaching image so that you understand each and every step.

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A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

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A: I am attaching image so that you understand each and every step.

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get