Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t = 0 1 1 1 T(0) = V3' V3' V3 1 1 0> N(0) = %3D

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A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

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Q: 8. Find y'if y = x³ +sin (x)

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Q: A curve y = f(x) have length of the curve from x = 0 to x = 1/2. dy Vcos(2x – 2) as its first…

A: We have to find

Q: 5. Calculate the following derivative x = 3e d y %3D Find (1) y=2e [y= 2e' ; dx? %3D dy 2) Let the…

A: (1) Given x=3e-t  and   y=2et The objective is to find d2ydx2. Now, dxdt=-3e-t and dydt=2et Then…

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Q: 3y' –4x²y+ xy = -5 %3D

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Which of these functions (or none of them): (1) z=e" (ycosx-xsiny) or (2) z=e' (y cosx-xsin x) 0²z…

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Q: (d) y = V1+r² + sinhr (e) f(r) = sinh Vr +1 (f) y = In coth 3.r

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Q: Find f. f "(t) = 5e + 8 sin t, f(0) = 0, f(x) = 0 f(t) :

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Q: Find dy/dx ln(x+y)-cos2y-x^2=0

A: Revise this before doing the question:

Q: Find f. f"(0) = sin(0) + cos(8), f(0) = 5, f'(0) = 2

A: Given, f"(θ)=sinθ+cosθ f(0)=5 and f'(0)=2

Q: y" – y' – 2y = sin 3t y(0) = 1 and y'(0) = -1

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Q: 3 Parameterize y(x) = +1 using x = t sin x Ans=

A: The answer is: y(t) = (-3/sin(-3/sinx) + 1)) + 1Explanation:To answer this question, you just have…

Q: 2. Find dy/dx: a. 3x? – (xy²)½ = 2y³ b. у%3D (сosx — ях)4x*

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Q: Can you find f

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Q: Find f. f '(x) = cos(x), f(0) = 6, f '(0) = 3, f "(0) = 5

A: Differential equation: f'''(x)=cosx f(0)=6, f'(0)=3 f''(0)=5

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Q: dy Find for y= csc (x)+ dx cos (x'+1). Do not simplify your answer. dy dx Given the equation x' + y'…

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Q: Find y'. CSC CSc t y=5+t cos t y' = %3D

A: As per our guidelines, I am solving one question please repost other question. y=csc t5+t cos tto…