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

Q: rrent Attempt in Progress Evaluate the line integral using Green's Theorem and check the answer by…

A: Greens theorem

Q: Sketch the region enclosed by y = 4x and y = 7x². Decide whether to inte with respect to x or y.…

A: we have to find the area of the region .

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) (x² + lim x + 5…

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Q: Graph in radians please

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 5ytx²j+4z² div F= curl F=

A:

Q: Verify the Divergence Theorem by evaluating F.N dS as a surface integral and as a triple integral.…

A: Here, using the Divergence Theorem, ∯F·Nds=∫∫∫v∇·Fdv Here, F=xy,z,x+y So, ∇·F=∂F∂x,∂F∂y,∂F∂z=y,0,0

Q: Find the distance from the point to the plane. (5,7,6), 10y +z= 0 The distance is

A: We can find the distance as below.

Q: A. Plane Area in Rectangular Coordinates Find the area bounded by the given curves. Sketch the…

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Q: 2. sin 2wcos 2wchw

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Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , eº cos u , e¯ ) at the point where u…

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Q: Find the indefinite integral. (Use C for the constant of integration.) 6 + 9x dx (x8 + 1)e*³.

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Q: Solve the problem. Solve the differential equation model of a population growth: dP 0.5P. dt O P(t)…

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Q: dy onsider the differential equation dx y? ) Re-write the equation in terms of differentials: dy =…

A: Given query is to find the solution of the differential equation.

Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

A: Given : f(x)=7x+1   To Find : a) Derivative of f(x) b) Tangent at point (a,f(a)) where a=5

Q: Evaluate the integral by making the given substitution. (5x)tan(5x)dx, u = 5x + C

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Q: Find the function y = y(x) (for x > 0) which satisfies the separable differential equation dy 4+ 12x…

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Q: dx 3-x

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Q: dx 2. o (x-1) 5

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Q: Find div F and curl F if F(x, y, z) = 13y'2*i – 11x°z®j – 7xy°k. %3D div F= 0 curl F=|(-35 z y³ + 99…

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Q: Evaluate the integral. V3/2 dr V1- r2 |

A: We know, ∫dx1-x2=sin-1(x)

Q: Improper Integral. KINDLY EVALUATE and Identufy whether convergent or divergent

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Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. 1. dx dx 2. xV4-x?

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Q: Find the indefinite integral by using the substitution x = 8 tan(0). (Use C for the constant of…

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Q: Kindly

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) COS X dx (sin x)20

A: Given, ∫cosxsinx20dx We have to evaluate the indefinite integral.

Q: EXAMPLE 6 Evaluate the following integral. tan (r) dr SOLUTION First we write tangent in terms of…

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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: Find the work done by F in moving a particle once counterclockwise around the given curve. F= (x-…

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Q: -dx is an improper integral. A True B) False

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Q: ​(A) Find the average value of the function over the indicated interval.   ​(B) Graph the function…

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Q: Find the divergence of the vector field F. F(x, y) = 8xe*i – 7x²y²j |

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Q: y = 4e2x + xe2x; y" - 2y' + 1 = 0. Yes O No

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(In 12x) dx Cos In x +…

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Q: 7 dx x² + 52 Integrate: + C

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Q: Find the general solution of the equation. Express the solution explicitly as a function of the…

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Q: dx (r-1)%

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Q: x2 + xy? lim (x,y)→(1,2) x4 + 2y2 or show that it does not exist. 2. (a) Evaluate the limit + xy? or…

A: We need to find limit.

Q: Determine whether the series converges or diverges.

A: Solve the following

Q: coso de by trigonometric substitution.

A: answer is in next step

Q: Evaluate the following definite integrals. år 5.

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Q: 1) What are the equations (4 of them) that show the relationship between polar and rectangular…

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Q: 10 8 10 f (x) dr=17 and f (x) dr = 12, then f (x) dx=5. A True B False

A: we use the properties of definite integral

Q: | h(r)dr 19 and | h(r)dr = 8.3 what does the following integral equal? h(r)dr =

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Q: Find the 73rd derivative of the function f(x) = 2 sin(x). f (73) (x)

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Q: Find div F and curl F if F(x, y, z) = x²i – 10j + yzk. div F= curl F=

A: As w e know that; The expression for the divergence of vector point function F→=F1i+F2j+F3k is: div…

Q: Solve the seperable differential equation 10yy' = x. Use the following initial condition: y(10) = 7.…

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Q: Evaluate the definite integral. (Round your answer to two decimal places.) 1 9 (cosh(x))² dx

A: cos h(2x)=cos h2x +sin h2xcos h(2x)=2cos h2x -1cos h(2x)=1+2sin h2xcos h2x =1+ cos h (2x)2

Q: Determine wnetner the function Isa linear transrormation. T: R2 - R³, T(x, y) = (x², 3xy, 2y²)…

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Q: (a) rªr- (b) y2 (c) e-4z+3e7z=3 ,71–3 (d) In(ez)

A: we have to simplify