farctan(6y) dy: Consider the integral 1+ 36y2 This can be transformed into a basic integral by letting and u = du dy After perfroming the substitution, you obtain the integral du

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. 2…

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Q: 2) 2x2 csck) dy %3D CS )ゾー XeJx-2 メ-2

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Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

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Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabo arc y = x² from (0,0) to (1, 1).…

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Q: Find curl (3z i + 4x j+ 7y k). curl (3z i+ 4x j+ 7y k) = ( i )i + ( i j+ ( )k

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Q: Find V · (V × F), if F(x, y, z) = 2e"²i+ 2xe"j – 9ev²k. V· (V × F) =

A: Given F(x,y,z)=2exzi→+2xeyj→-9eyzk→ To find, ∇.(∇×F)

Q: Find div F and curl F if F(z, y, z) = 9e#i-9 cosyj+3sin? z k. %3D div F = curl F=

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Q: Find the arc length of the parametric curve. x = e', y = et, z = v2t; 0<t< 7 L = e - e- - 0

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Q: for x[z] given by z1 x[z]: 1-z2 then X[00] equal to Select one: a. 0.5 b. 0

A: B is the correct option.

Q: Line segment AB is a diameter of the x² +y² + z² - 2z + 8y = 9. Find point B if A = (0, у, 0).

A: To find the point B if Coordinates  of A are given for the sphere.

Q: 1 f. dx Vx(Vx + 2)

A: Find your answer below

Q: Definite Integral. 2.) S x²(2x³ + 1)*dx 4.) x?e*dx 6.) f- xp:

A: To integrate.

Q: ) Syppose f and g are functions with continuous lerivatives, and that they satisty the following. S…

A: Let's find.

Q: 4. Let em² cos , 2.x + b, r 0 r>0 h(x) = %3D where b is a constant. (a) Explain why h(x) is…

A: We need to solve continuity problem.

Q: Use the following graph to answer the questions that follow. 325 Domestic supply 275 225 Price of…

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Q: 3 d : 4me-m2 dy. dm

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Q: Solve the differential equation Integrating Factor by Inspection: (2y – 3x)dx + xdy = 0

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Q: 5 1. If g(2) = 59 and , g'(x)dx = 25, what is g(5)?

A: The detailed solution is given below Thank you

Q: y" + 2y' + 5y = 4e¬t cos 2t, y(0) = 1, y'(0) = 0 %3|

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Q: Describe the graph of the equation. r = - 2i + tj + (t² – 1)k O Itis a parabola in the x = 2 plane,…

A: Here we  have to identify the vector.

Q: Hi there, please help me with answering this question. I am a bit confused here. It would be highly…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: This is a problem related to vector calculus. Based on the general formula of green's theorem we…

Q: 2. SET-UP the definite integral that will give the area of the region specified using (a) x as the…

A: Area

Q: Follow the instructions. Typewritten for upvote. No upvote for handwritten. Thank you

A: We have to find the number

Q: Solve the following differential equations of e • dx+2(xe" – y)dy = 0;

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Q: 524–121x4 lim x00 62xº+24x4+234x³+11x2+169 ||

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Q: Solve d 4me-m2 dy dm

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Q: 1.) ° 6x3+4x²-8x dx I. Evaluate the following Definite Integral. 1.) ° 6x³+4x²-8x 2.) x²(2x3 + 1)Fdx…

A: we want to find the integral ∫03( 3x-6 -1 )  dx

Q: Write the binomial expansion for the following expression. (1*+1) 5 (1* +1)° = (Simplify your…

A: To write the binomial expansion.

Q: Find V x (V × F) if F(x, y, z) = 9xyj+ 5xyz k. V x (V × F)

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Q: I. Evaluate the following Definite 1.) Sº 6x³+4x²-8x 1.) L,º 2x 3) (3 sin3(x)dr

A: According to rules.. I  need to solve 1st question

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = t'i+ t°j K(t)

A: The given formula is; κt=r't×r''tr't3 And rt=t2i+t9j

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 3…

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Q: Solve the differential equation Integrating Factor by Inspection: (x* – y*)dx + xy³dy = 0

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Q: Given u = ( 5, -3, 8) and v (k, 2, 4) calculate k, by using only vector | = 2 7| concepts, where…

A: Topic = Vector

Q: A farmer finds that if she plants 40 trees per acre, each tree will yield 20 bushels of fruit. She…

A: Harvest

Q: Given r = (5, 2, 3) and s = (-4, -2, 2) and t = (3, 4, 1) %3D a. Write the unit vector for S b.…

A: This question can be solved using the concept of unit vector and linear combination of vectors.

Q: 5. The denominator of a fraction is four less than the numerator. If the denominator is doubled and…

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Q: Evaluate the double integral. / 5x(4 + y) dA; R R is the region in the first quadrant enclosed by y…

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Q: Solve the differential equation Integrating Factor by Linear Equation: dy 1 dx x + y2

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Q: 5.) Find the volume generated by revolving the area bounded by the curve y2=4x, x = 0 about the line…

A: Given area is bounded by: y2=4x and x=0. The area is revolving around the line y=4. From y2=4x we…

Q: Find the sum of the first n terms of the following arithmetic sequence. a1 = 2, d = - 4; n = 6 O A.…

A: Given problem:- a1 = 2 ,d = -4 ,n=6  To find:-  Sum of n terms of given arithmetic sequence

Q: Evaluate the expression. 12 O A. 66 О в. 6 О с. 33 O D. 239,500,800

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Q: Find V. (V x F), if F(x, y, z) = 6e"²i+ 3xe"j – 6e²k. - V· (V × F) %3D

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Find the partial derivative. revIlzy

A: We can find the partial derivative as below.

Q: letter b

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Q: Solve the differential equation Integrating Factor by Linear Equation: (xy² + x²)dy + xydx = 0 %3D

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Q: Hi, I believe the function was not entered correctly in the transcription. It should be x^2-16/x-2.…

A: Apologies for the inconvenience. First two steps were correct in the original solution. Step 3 was…