Solve the equation y' = csc(x) - y cot(x).

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A:

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A: Let's find.

Q: Find fxy for the function f(x, y) = V3x²y + 5.

A: The given function is f(x)=sqrt(3x2y+5).

Q: sin Inx 12. S dx x cos² In x

A: Given integration is ∫sinlnxxcos2lnxdx We solve the integral using proper substitution.

Q: y10) f(x, у) %3D In x9

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Q: Find f, and f, as functions if 2y f(x. y) = y+ y + cos x

A: This question is related to differentiation, We will solve it using given information.

Q: Show that fu,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the…

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Q: Use the Shell Method to find the volume of the solid obtained by rotating region above the graph of…

A: Given: fx=y=x2+2, y=18 and  0≤x≤4 And the bounded region is: Apply the shell method to find the…

Q: Use the substitution method to find all solutions of the system of equations. S2x + y = 5 x + 2y = 1

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Q: Match the graphs with the corresponding formulas. 1. Sn = 2 – 1/n 2. Sn = 2+1/n ? v 3. Sn = 2+…

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t=0 %3D 1 1 1 T(0) %3D V3…

A: Let's find.

Q: Find a formula for Sn, n > 1, if sn is given by 6 7 3' 5' 7' 9' 11 4 8 - Sn =

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Q: 9. sin ở In(cos 0) de

A: let I=∫sin θ ln(cosθ) dθ Integration By parts: ∫udu=uv-∫vdu u=ln( cosθ) ; du=1 cosθ-sinθdθ=-tanθdθ…

Q: tind ds 3\nx when

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The slope of a curve at any point (x,y) is given by dy/dx= 8 - x.  If (2,14) lies on the curve, find…

A: find the equation of the curve.

Q: Find the absolute maximum and minimum values of f(x) = e * – 3x on [0,5].

A: f(x)=ex-3x Take derivative wrt to x f'(x)= ex-3

Q: Plot the point whose polar coordinates are -3, In the graph below, use the 4. options to change the…

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Q: stone dropped into a still pond sends out a circular ripple whose radius increases at a constant…

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Q: (-3,-).* Plot the point whose polar coordinates are (-3, . In the graph below, use the options to…

A: Given problem:- Plot the point on graph whose polar coordinates are (-3, -π/6)

Q: "Suppose w =+, x = cos² t, y = sin? t, z = dw Evaluate at t = 3, by using the Chain Rule dt

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Q: B(4, 4) A (2, 0) /2 3 4 5 6 -2 寸

A: We have to solve given Questions.

Q: Find the partial derivative of f(x, y) 8x - 2xy2 + y3 with respect to x at the point (2, 1, 61).

A:

Q: 35. A hallway of width a = 5 ft meets a hallway of width b = 4 ft at a right angle. Find the length…

A: Given problem:-

Q: 6. For each function determine: i) the critical values ii) the intervals of increasing or decreasing…

A: 6 A)

Q: Identify the graph of the curve by first sketching the graph of r as a func Cartesian coordinates. r…

A: r=2-2cos(θ)

Q: Find the equation of the sphere

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Q: Let f : R → R be an odd differentiable function. Define F: R2 → R by F(x, y) = f(x² + xy+9y²). (a)…

A: This is a problem of differentiating function. Based on the concept of partial differentiation we…

Q: 8. Evaluate the limit of (4x^2-x)/ (2x^2+4) as x approaches a. a. 2 b. 4 с. а

A: We have to find limit.

Q: Determine the Laplace transform of the following function f(x) = x2 1.

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Q: Find polar coordinates to represent (-2, -2) with r >0 and 0 <0< 2T.

A: Cartesian to polar conversion (x,y)→(r,θ) where r=x2+y2 θ=tan-1yx

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Q: Draw an image o

A: answer is in next step

Q: Find the inverse of the function on the given domain. f (z) = (x – 14)2, [14, 0) f-1 (2) =

A: The given function is;  f(x)=(x-14) 2,[14,infinity).

Q: 5 (b). ( the base radius making the surface area minimum. ) Consider a cylinder having fixed volume.…

A: Use the application of derivative to minimise the surface area.

Q: any solutions does the equation 2 + 6 (x 4) = 3x - 18 + 3x have?

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Q: V10 – Vx dx 3 2x2

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Q: Either show that the improper integral converges and find its value, or show that it diverges S* the…

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Q: * This matrix is a -7 -5 11 7 -11 diagional matrix symmetric matrix An upper triangular matrix skew…

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Q: Given G(x) = jin(2t+1)dt , find G '(x). O In(2x + 1) O In(2x + 1) - In3 O In(2t + 1) + C 2 2x+1

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Q: taylor tan)

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Q: 2pm travels east at 50 mph. How fast are the trains separating after a long time?

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Q: 15. The solution of Laplace equation и + 3 0, и(х,0) — 0, и(х, п) — 0, и (о, у) — 0, и(0, у) %— 3sin…

A: Please see the below picture for detailed solution.

Q: Use a double integral to find the volume under the plane z = 20x + yand over the rectangle R {(x,…

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Q: Solve the equation .11 y" + 3y' + 2y = x2

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Q: The surface area of a closed box is 200 square feet. If the width and height have the same…

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Q: 3 4x Evaluate -dx. 4 2 x'-6 3 4x -dx = x* -6 4 (Round to the nearest thousandth.)

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Q: Q3. Given the complex numbers z1 = -V3 +i,z2 = 2-i,z3 = -V3- 3i and z4 = 4 + 4i %3D 3.1 Represent…

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Q: Find the general solution of the second-order differential equation: 4y" – 4y' + 13y = 0.

A: We have to find the solutions

Q: Test the series for convergence or divergence. 4 6. 8 10 .... 7 8 10 11

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Q: Given an area of circle of 96 inches squared, determine its given radius by using the initial…

A: This is a problem related to numerical method. Based on the initial value of the radius we will…