Find V · (V × F) if F(x, y, z) = 7 sin xi + 10 cos(4x – 5y)j+ 5zk.

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A: we have to find curl and divergence of F.

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A: The given integral is: I=∫x3dxx2-4

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Q: | (ax³+ bx² + cx) dx = 2b x²dx where a, b and c are constants. (A) True B False

A: We need to show in this question whether the two integrals are equal or not

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Q: Solve the system of differential equations x' 4x – 15y ly' 2а — 7у - x(0) = 3, y(0) = 1 x(t) = y(t)…

A: We solve the given problem using method of elimination by use of operator D  .

Q: raluate the following definite integrals.

A: Topic:- definite integration

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Q: Sketch the region enclosed by y 6x and 4x. Find the area of the region.

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Q: Use the formula k(t) |r(t) × r"(t)|| x r" (t)|| to find «(t). ||r(t)||° r(t) = ti+ t5j «(t)

A: To find k(t).

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Q: Question 6 Determine the derivative, y': y = log, (In a?) %3D Oy = z In 5 In a Oy = = z In 5 In z Oy…

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Q: d 3 4тe-m? dy -m² dm y

A: Note that, the fundamental theorem of calculus says: If F(y)=∫ayf(m) dm then ddy∫ayf(m) dm=f(y)

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Q: In |V Vr+i-2 dt, if we let / Vr+1 - 2, then dt is equal to A 4x°dx None 2(x²+ 2)dx (4x³ + 2)dx E…

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Q: Use the Divergence Theorem to compute the net outward flux of the field F = (4x, y, - 2z) across the…

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Q: Consider the following function. T: R2 → R3, T(x, y) = (2x², 2xy, 2y²) Find the following images for…

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Q: 21 3x7 + 8x 5x

A: Given: y=3x7+8x5-215x

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Q: Use the below graph of f(x) defined on the interval (0,12] to answer 4 through #9. 4- 11 4) Over…

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Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We want (x,y,z) such that 6x2+y2-3z2=4 and ∇f(x,y,z)=λ(2i→+7j→-k→) for some λ where…

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Q: Calculus Use newtons method with the specified initial approximation x1 to find x3 the third…

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Q: Find the integral. 4 9) x4 In 2x dx A) 391.74 B) -202

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Q: 21 Given 3x7 +8x5 - , determine, y" O 630x4 + 480x² + 126 5x4 O 840x3 + 360x 504 - 504 O 2520x3 +…

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Q: Find y': %3D Oy =- Oy=--

A: A detailed solution is given below

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Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

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Q: S*r(sin³x cos x + sin x cos x) dx -- 4 Ja sin 50 de

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Q: The derivative with respect to x of | (3Vi-1) dr is 3x – 1 by the 2nd fundamental theorem of…

A: Given that,         ∫3x3t-1dt

Q: is an improper integrat. dr A True B False

A: To check : The statement "∫-121x2dx is an improper integral." is True or False ?

Q: Solve

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Q: Find y': y = ar cos

A: The given function,  y=ar cosx3

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Q: Given a function f(x, y) = In(9 – x² – y²). (a) Find and sketch the domain of the function. (b) Find…

A: Given function f(x,y)=ln(9-x2-y2 )

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Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

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