Given: parametric curve H defined by x(t) = tan¯¹t and y(t) = e¹t, where t € R (a) Find the slope of the normal line to H at t = 0. (b) SET-UP the integral which yields the arc length of H from (0, 1) to (, e4).

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A: We can check the false option as below.

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A: Solution:

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A: SOLUTION-

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A: We will solve the problem

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A: We find the line integral in the following way

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A: We will solve the problem

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A: all continuous functions have antiderivative.  But noncontinous function doesn't have. It's true

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A: SOLUTION-

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A: Please refer to the image below

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A: Given problem:-

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A: Please refer to the image below

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A: Applications of differentiation

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If R(0) = (-1,4,-5),…

A: