Determine the vector field of F. F(x, y) = yi - xj

Q: Define Euler's number e. Sketch the graphs of the function f(x) = at are the domains and the ranges…

A: answer is in next step

Q: Ay 4- 2- -> 4 -2-

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Q: 1 The partial derivative of f(x, y, z) = Arctan with respect to z is xy? z³

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Q: Evaluate the definite integral. ¤(x² + 7)°dx (b) / z x/1 – x²dx (a)

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Q: Find the cost function if the marginal cost function is given by C'(x) = x3 +4 and 27 units cost…

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Q: www 1D syppose that a sequence CanZ is definel by the envations az =2 cand anti = following is true…

A: Clearly,

Q: Qg Solve: coshx-1 .dx

A: Basic hyperbolic identities are used along with integration identities.

Q: -3 2. (2x+4)3 8x dX use integration by parts and then find the value of definite integral.

A: A detailed solution is given below.

Q: Evaluate the definite integral

A: Given∫pi/40sin62wcos62wdw,

Q: Determine whether the series converges or diverges.

A: Solve the following

Q: f(x) z400 g(x) lim where f(r) and g(x) are seen in the graph. 3 S(x) 2 -5 -4 -3 -2 -1, 2 9(x)

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Q: lim 2?e --00 1- cos(2x) im

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Q: The graph of the function f(x) = sin(x+ 8) is shown along with the points (– 8, f( – 8)) and (– 7,…

A: (1) f(x)=sin(x+8)f'(x)=cos(x+8)slope =f'(-8)=cos(0)=1equation of tangent at…

Q: 2. Given the DE as (x² + y² – 3)dx – 2xydy = 0 a) Prove if the given DE is exact or non-exact b)…

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Q: Question 9 Solve the problem. Find the volume of the region enclosed by the sphere x2 + y2+ z2 = 100…

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Q: Find each of the following limits. Since you use L'Hopitals Rule, explain why you use it lim 2?e…

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Q: Find div F and curl F if F(r, y, z) = 13y"2°i – 11a2°j – 7xy°k. div F= curl F=

A: We have to find the  divF and curl F

Q: 2. sin 2wcos 2wchw

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Q: Question 18 Find the length of the curve with the given vector equation. r(t) = (6 + 2t 3) i + (2t…

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Q: Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. f(x) = cot x, a = - Po(x)…

A: As we know that; The Taylor series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+… Where centered at x=a.…

Q: 9. 5+ 8 7- 6- 3 5 4 2 g(x) 2 h(x) 1 1 1 2 3 x-values 4 5 1 2 3 x-values 4 If f(x) = g(h(x)), then…

A: Explanation of the answer is as follows

Q: (2+금) 3 29 7. Suppose that lim In Fill in the boxes for the corresponding equation -- - - '(2+금)% n…

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Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

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Q: Evaluate the following improper integrals. Tell whether it is convergent or divergent. dx

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Q: 6. Evaluate the indefinite integral as an infinite series. (b) / sin z (a) / r cos(r)dr

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Q: x + 4 1. Evaluate dx. Vr2 + 8.x

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Q: Write an iterated integral for J dA over the region R described to the right using R a. vertical…

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Q: cos*x _8. If S(cos x B) dx = - +C, what is the B? A. - sin x C. COs X В. D. cscx secx Which

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Q: Solve the differential equation for general solution dy = - dx V y = 14x + C O y = /14x + C, or y =…

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Q: Evaluate the integral by making the appropriate substitution: u = NOTE: Your answer should be in…

A: On solving this we will get:-

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: The astroid curve below is defined by the parametric equations x(t) = 2 cos' t, y(t) =2sin't.…

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Q: 4. Suppose that f(2) = 16 and that f'(x) > – 3 for all x in the interval [2,7]. Determine the…

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Q: Find the equation of the plane perpendicular to the line x 2t, y = 6 - t, z = 4+t and containing the…

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Q: If y= (x+1). sech (Inx) find dy ノ

A: Use the product rule and chain rule of derivative.

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: Q2: You have the matrix How can we get the transpose matrix

A: Given problem:-

Q: 2. A turns 100 RPM and B 150 RPM as shown; they are connected by rolling cones. Calculate the cone…

A: Solution: wa = 100 rpm wb = 150 rpm

Q: The company can sell the item for $90,000 each. a) Write a cost function C(x) and a revenue function…

A: Given query is to find cost function, revenue function and profit function.

Q: The partial derivative of f(x, y) = e"y – 2x – 4y + 3 with respect to x is O ye"V – 2 af af ery + y…

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Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A: Using Euler's Method we have  xn = xn-1 + h  yn = yn-1 + h . f(xn-1, yn-1)  In the given question we…

Q: .1//7 7 arccos x x² dx V1- x 1 –

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Q: Find the unit tangent vector to the curve at the specified value of the paramet r(t) = 4 cos(t)i + 4…

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Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: 7. Give one example a that makes log, (x) rational but not an integer

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A: Given,  ∫1+∞1xdx

Q: 6. (ax3+ bx2+cx) dx= 2b | x2dx where a,b and c are constants. -9 A) True B False

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Q: Find the tangent line approximation T to the graph of f at the given point. Then complete the table.…

A: Solution:

Q: uestion 19 Describe the largest set S on which it is correct to say that f is continuous. f(x, y, z)…

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Q: Question 14 Find the volume of the indicated region by an iterated integration. The region that lies…

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