Find the partial derivatives of f (x, y) = 5x°y². %3D (a) fa(x,y) = (b) fy(x, y) (c) fa(3, y) = %3D

Q: Find div F and curl F if F(c, y, z) = 10e*Y i – 9 cos yj+ 4sin? z k. div F= curl F=

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Q: Use the given vectors to find v•w and v.v. v = 61 - 4), w= - 21 -J v•w= 2 (Simplify your answer.)…

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Q: Find V. (V × F) if F(x, y, z) = 7 sin xi + 2 cos(2x – 3y)j+ 6zk. V·(V × F)

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Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. dx x²V4-x2

A: The given integral is 1/[x2 sqrt(4-x2)].

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Q: x³dx is equivalent to x² – 4 Using trigonometric substitution , A sec+0 do B) None © 8 C sin³e de D…

A: The given integral,        ∫x3dxx2-4

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A: answer is in next step

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Q: One of the correct. steps to evaluate x²inx. x²Inx dx to yield the correct integral (A dx x2Inx B x³…

A: The given integral,     ∫x2lnx dx

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Q: Find the coordinates of the centroid of the given figure. Each region is covered by a thin, flat…

A: Solved below

Q: dx 2. x?V4-x2

A: Let x=2sin(u)⇒dxdu=2cos(u)⇒dx=2cos(u) du  and u=sin-1x2 ∫dxx24-x2=∫2cos(u) 2sin(u)24-2sin(u)2du…

Q: 4. Use partial fraction decomposition to evaluate dx x' + 4x +3 2

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Q: For the given cost function C(I) = 128/ + find 512000 d) The production level that will minimize the…

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Q: ||r(t) x r"(t)|| ||r'(t)||* Use the formula K(t) to find K(t). r(t) = 4 cos(7t)i+ 4 sin(7t)j + 3tk…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti +t dt

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Q: The general solution of the differential equation dy/dx 12x is y = 4x + C. Select one: O True O…

A: A separable differential equation can be written is of the form of dydx=f(x)g(y).

Q: r arcsin(5y) dy. Consider the integral V1– 25y? This can be transformed into a basic integral by…

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Q: A box with a square base and open top must have a volume of 415292 cm. We wish to find the…

A: topic - application of derivatives

Q: Find the general solution of y' =y sec x. A. y = C (secx+ tan x) B. y= C (sec x – tan x) C. y = C…

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Q: ||F(t) × r"(t)|| ||r(t)||* Use the formula k(t) = to find k(t). r(t) = e""i+e-tj K(t)

A: To find out the k(t).

Q: L 32 da = 65 %3D Select one: O True O False A2Vadx = 104/3 Select one: O True O False S (+4)(a+3)da…

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Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. 1. dx

A: see below the answer and calculation with steps

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Q: The general solution of the differential equation dy/dx = 12x³ is y = 4x3 + C. Select one: O True O…

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Q: Suppose a population function P(t)  the following differential equation. P is measured in millions…

A: Given dPdt = P(P-10) The slope field is plotted in Desmos slope field generator

Q: Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other…

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Q: Find the area of the plane region bounded by y = x - 4x and y% x(2-x). Answer

A: As per Bartley guidelines we are supposed to answer only one question per post.  This post contains…

Q: You want to build a 1100 square foot rectangular infinity pool. Three of the sides will have regular…

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Q: Evaluste the line integral using Green's Theorem and check the answer by evaluating it directly.…

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Q: Find V (F × G), if F(x, y, z) = 11xi+j+3yk and G(x, y, z) = xi + yj – zk. V. (F x G) = %3D

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Q: Describe the graph of the equation. r = 3 cos t i – 18 sin tj+ k O An ellipse in the plane z = 1,…

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Q: 3 dy – sin-! 3y -12+C %3D sin-1. 4- 9y 3

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Q: The following differential equation is exact. Find the general solution. (7x + 6y) dx + (6x − 8y3)…

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Q: S- (1+x²) = x*dx Using trigonometric substitution, tan ode A sece sin Ode B cose S tan od0 sec20 sec…

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Q: Find the magnitude Iv|| and the direction angle 0 for the given vector v. v= - 7i+ 10j ... (Round to…

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Q: The particular solution that satisfies the differential equation and the initial condition dy/dx =…

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Q: 2. Evaluate f'(5) for y = v2x² – 1

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Q: Solve the following initial value problem by using the Laplace Transform method. y'' − y' = ex,…

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Q: A restaurant has an annual demand for 884 bottles of California wine. It costs $3 to store 1 bottle…

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Q: sin' (12x) dx =

A: TO find : ∫sin3(12x)dx=?

Q: i cos tdt can best be evaluated by: A Trigonometric Formula B) None C) Integration by Parts D Power…

A: Since multiple questions are asked,I am doing first question