If r(t) = (tº, t, t²), find r’(t), T(1), r”(t), and r'(t) × r”(t). 9t³i+j+ 2tk r' (t) T(1) = = 9i+j + 2k √86 r"(t) 72t7i+0j + 2k = r'(t) × r²(t) = −(144t³ — 162t¹6)j + (72t7 — 81,¹6) k X

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A: The objective of the question is evaluate the definite integral and rewriting the integral.

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A: To find f"(t) we integrate f"'(t)

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A: We will use parameterization to find line integral

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A: Given fi=5,f'i=-3i,gi=3i,g'i=4. Find fg'i.

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A:

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A: Solve for the angle X

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A:

Q: B) If f (x, y) = tan (2x – 3y) find дх ду?

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A:

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A:

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A:

Q: If fxy (x, y) = y for 0 2X - 2) =

A:

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A: Note: As per the guidelines, I have solved three sub-parts. If you want the solution to the last…

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A: Given:rt=sint , t2, t2+1-1

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A:

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A:

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A: Leibnitz Theorem