Evaluate the line integral / (6x + 8y)dx + (4x – 8y)dy along the curve C: x = 2 cos t, y = 4 sint (0

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: bounded by the graphs of the equat y

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Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

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Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

A: We have to find the conservative vector field.

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

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Q: -6w + x + 3y + 6z = -6 -7w - x – 9y – 2z = -33 -4w – 9x + 8y + 9z = -94 -w – 6x – 10y + 9z = -202…

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ei + Sin(/2)j + e stk…

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Q: (a) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) =…

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Q: Question 13 2 Evaluate the iterated integral. yz dx dz dy

A: Evaluate the iterated integral .

Q: Question 7 Find the area of the region(s) enclosed by the curve f(x) = x³, the x-axis, and the lines…

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Q: Determine the volume generated when the area bounded by the curves y = sin x and y = cos x from x =…

A: Given problem:- Determine the volume generated when the area bounded by the curves y = sin x and y =…

Q: Use the Product and Quotient Rules as necessary to find the derivative of f(x) = 7x? cos(x) (Use…

A: The given function,      fx=7x2cosx

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A: Let's find.

Q: 1- sine Evaluate the iterated integrals J. J. r2 cose dr de̟ A ) 1 В 2 (c) o D 3

A: The integration of the double integral is r2Cos(theta).

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Use Ore's theorem to prove that any n-vertex graph G for which |E(G)|> (",') +2 is Hamiltonian.

A: answer is in next step

Q: a) Consider the scalar function: f(x, y) = -4x*y³ – 2a*y? Find the gradient: Vf(x, y) = i+ Find the…

A: Given; f(x,y)=-4x^2y^3-2x^4y^2

Q: Find the divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

Q: 1009 1010 Suppose R= E (2k) = 2 + 4 +6+.+2018 and S= D (2k-1) =1+3+ 5+.. + 2019 What is the value of…

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Q: In sketching the graph of y=f(x) = 2sin -5, we translate the graph of y=2sin by 5 units downward and…

A: To translate the given function.

Q: The function ƒ (x) = |x| is continuous at every real number. %3D False True

A: Let's find.

Q: Find the area of the region(s) enclosed by the curve (x) the x-axis, and the lines x = -1 and X= 2.…

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Q: O An ellipse in the plane x axis, minor axis of length 14 parallel to the y-axis. = 1, center at (1,…

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Q: 102: Find div F and curl F if F(x, y, z) = xz°i+ 5y1ºx²j+4z²yk. div F = curl F=

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Q: A spring has a natural length of 22in. A force of 16001b stretches the spring to 32 in. How far…

A: We will use rules of spring stretch to solve it.

Q: +1++4+ +7++10 written in sigma notation is equal to The sum 3k-5 A k=1 3k - 4 B k=1 3k-2 k=1 3k-1…

A: Let's find.

Q: Find the area of the region(s) enclosed by the curv

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Q: Express the area of the given surface as an iterated double integral, and then find the surface…

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Q: п! n4 n=1

A: The given series is: ∑n=1∞n!n4 Let, an=n!n4; n≥1

Q: 2. Sheldon is being chased back-and-forth by a dog along Euclid Avenue. His directed distance (in…

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Q: Solve the following differential equations of 1- yy' = 2y – x; r'y'y'+ xy' = 1 dy x + v

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Q: e

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Q: Find div F and curl F if F(x, Y, z) = xz°i+ 2y°x²j+ 2z²yk. 6 div F= curl F =

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Q: Evaluate the integral. NOTE: Enter the exact answer. xe* dy dr =

A: the integration of the double integral is xexy.

Q: Calculate x sin(y)dxdy

A: On solving this we will get

Q: Question 5 Find the surface area of that portion of the surface z = V4 -x that lies above the…

A: Option (B) is correct

Q: 7-18 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7.…

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Q: find SCE) at timet V=-5t+5, S0) = 14

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Q: Find the Laplace transform of f(t) ={0, 0 ≤t ≤1         7t −7, t ≥1 .}

A: Given :f(t)=00≤t≤17t-7t≥1

Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt dt the product directly…

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Q: find in Verse, then domain t range 8-X\ = (x)} OD:[8,8),R:[O,00) 2 All Real Numbers 8.00

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Q: Find the area of the region enclosed by x2 and y = 5x by integrating with respect to y. the curves Y…

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Q: For each of the following series determine if the series converges or diverges. 00 In(n) Σ n n=2 n3…

A: The given series,1. ∑n=2∞ln(n)n2. ∑n=0∞n3n4+1

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A: Let's find.

Q: 3. The speed of traffic through the Lincoln Tunnel depends on the density of the traffic. Let S be…

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