Find the directional derivative of the function at the given point in the direction of the vector v. g(u, v) = u²e-v, (8,0), v = 3i + 4j Dvg(8,0) =

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A: Length of rectangle=x ft Width of rectangle=y ft Radius of semicircle r=x2ft

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A: triple integral

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A: According to question,Given Point : -5,1,2,Given Line : a⇀t = -5,0,-3t+-7,1,-5

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Q: If g(x)=√1+tdt, then find the derivative g'(x).

A: Given :- gx=∫0sinx1+tdt

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

Q: x(t) Find the point at which the line y(t) z(t) = = = 4 - 8t -4+ 5t intersects the yz plane. 6 + 2t

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Q: Find the sum of the convergent series. 00 Σ η = 1 8 gn2 + 3n - 2

A: According to question,Given Series,∑n=1∞ 89n2+3n-2

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A: Given: f(x) =5x3-54x2+170x-104 One of the zeroes of the the given function f(x) is 5+i

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A: integral

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Q: What is the vertical asymptote for the function f(x) = 1 4x Ⓒx=0 x = 1 x=4 y=1 ? 61

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Q: A solid is obtained by rotating the shaded region about the specified line. about the x-axis y 6…

A: see below the answer and calculation

Q: Consider the following power series. Let a = lim LIM R 11 (-1)*(x-8)* ku 11k (-1)* 11k (x-8)*. Find…

A: Solution will be given below

Q: 1. Let f: R→ R such that f(x) = -x ifa is rational and f(x) = 2x+3 if x is irrational. Prove that f…

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Q: 5. The Cobb-Douglas production function for a new product is given by P(x, y) = 10x406, where x is…

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Q: 3 Integrate f(x, y) = y(x² + y²)³ over the domain x² + y² ≤ 25, with y ≥ 0. Added 55 Pak Young FGS…

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Q: What are the solutions to the equation 3x² + 6x + 5 = 0? A B C D - 1 t −3+√6i 6 ± −1+ 3 i 2√6 ∙i w/²

A: 3x2+6x+5=0we know  -1=iwhere i is stand for iyota

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Q: 1. Let f(x)=√x. a) Find the linearization of f(x) = √√x at x = 16. b) Use the linearization from…

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Q: 5. Consider the region R bounded by y=1-x² x = 0 and y = 0 [This region is used to answer questions…

A: Draw the graph and then select the region.Take a small volume of a cross section area and integrate…

Q: Question 4 Evaluate (x + 1)e* dx by the method of integration by parts.

A: Given integration is ∫01(x+1)exdx

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Q: The table below shows the value, V, of an investment (in dollars) after n years. n 3 7 12 14 19 0…

A: Solution: By using exponential regression graph plotter

Q: Find the triple integral of the function f(x,y,z) = x2cos(y+z) over the cube 3<x<4,0<y<pi,0<z<pi.

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Q: Find the volume of the solid generated by revolving the region bounded y = sin x, y = 1 on the line…

A: To find the volume of the solid generated by revolving the region  bounded by y=sin x, y=1 on -3π2,…

Q: 6. Find the limit. Show your work algebraically. lim x48 (5 + 2/7)

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Q: Evaluate the integral Note: Use an upper-case "C" for the constant of integration. -2 12²=2² da

A: To evaluate the following integral. ∫-2x4x2-2 dx

Q: Find both first partial derivatives. sinh(5x + 13y) əz Әх əz ду || ||

A: To find partial derivatives

Q: 4. Find the value(s) of x at which each function is discontinuous. x² + 1 b. g(x) = 7x - 4 c. h(x) =…

A: See below the answer

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A: Give that, the quadratic formula allows us to find solutions to any quadratic equation. We have to…

Q: The graph of the first derivative f' of a function f is shown. (Assume the function is defined only…

A: Since, you have asked a question with multiple sub parts, as per company guidelines we will solve…

Q: You go to the doctor and he gives you 17 milligrams of radioactive dye. After 16 minutes, 5.25…

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Q: (b) (c) Ο Ο Ο Ο 0 Ο Ο Ο Ο 8+6=2 8 2 = 6 2+6=8 8 6 = 2 ( 6 + 2 = 8 L 8 1 8+6=2 +1 8 0 1 2 3 4 5 6 7 8…

A: To solve the following problem

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Q: QUESTION 1 If f(x) = 3x +51, - 1<x< II, Then the sum of the Fourier coefficients ao + b₁ + b₂ + b3…

A: A detailed solution is given below.

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Q: Find [[ cos (x² + y²) dA where D = {(x, y) | 9 ≤ x² + y² ≤ 25}

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Q: /transcript Perform a first derivative test on the function f(x) = x (x-3); [-3,3]. a. Locate the…

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Q: Find the interval(s) where f(x)=x²-3x³-6x² - 2x +4 is concave up.

A: Given function:- fx=x4-3x3-6x2-2x+4