Find the unit tangent vector at the indicated point of the vector function r(t) = e4t cos ti + et sin tj + e¹tk T (π/2) = (

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A: Given points : P(2,4,4), Q(3,1,6), R(2,8,0) and S(9,2,-1)

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A: Given; Limx-5(x+5)/(x2-25).

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Q: Tutorial Exercise Find the volume V of the solid obtained by rotating the region bounded by the…

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

Q: Solve the equation. A. x+9=-12 C. -0.3+r=4.7 B. -8+k--17 D. +3m= 12m

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and…

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A: Given rt=t, lnt, 0

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Q: 3. Consider the function: f(x)=√16- x² + 2 a) Sketch the graph. and Using geometric formulas…

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Q: Tutorial Exercise Find the volume V of the solid obtained by rotating the region bounded by the…

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A: Explanation of the answer is as follows

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Q: Use the graph to estimate the open intervals on which the function is increasing or decreasing.…

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A: Solution is given below:

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A: Given query is to find the derivative of the function.

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A: Topic:- calculus

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A: (a)  y-32=x-5

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A: The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis…

Q: Find the derivative of the vector function r(t) tax (b + tc), where a = (2, -5,-2), b = (4, 2,-5),…

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Q: Find the positive t when the vector →r(t)=⟨9t,9t2,9t2−23⟩ is perpendicular to →r'(t).

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Q: 1) In(x)x /√x² - 1dx.

A: The given integral is ln(x)x/sqrt(x2-1). Repost the next questions.

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A: solve the differential equation 3-xdydx=3

Q: 2. (a) (c) 1 x-5x+6 Evaluate - S In x-31 - In/x-2| + C In x-3| + In|x-2| + C -dx (b) (d)…

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A: We need to find asymptote.

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A: solution is given ...

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A: See the details solution in below

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Q: Find the domain and range of the function X (b) y = √2x + 3 (a) y = 2. If f(x) x + 3 2 = - X " g(x)…

A: Note: as per guidelines we support only three subparts of the questions.kindly repost next questions…

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A: Solution

Q: questions

A: *Note: As per policy only first question is answered. Question 4. Given: G(z) = (z-6)lnz