Consider the curve parameterized by ( x = 1 3 t 3 + 3t 2 + 2 3 y = t 3 ? t 2 for 0 ? t ? ? 5.

I’m working on a calculus test / quiz prep and need an explanation and answer to help me learn.

Consider the curve parameterized by ( x = 1 3 t 3 + 3t 2 + 2 3 y = t 3 ? t 2 for 0 ? t ? ? 5.

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(a). Find an equation for the line tangent to the curve when t = 1.

(b). Compute d 2y dx2 at t = 1.

(c). Write an integral to compute the total arc length of the curve. Do not evaluate the integral.