Let P be the point in R^3 with rectangular coordinates (√2, −√2, 2√3). How to find the cylindrical coordinates for P and the spherical coordinates for P.

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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A: Given the following differential equation: y' − 2y = (e^3x)/((e^x) + 1)

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Q: Determine whether the series Σ=1 (Limit Comparison Test) 2n²+3n √5+n5 converges or diverges.

A: Given :∑n=1∞2n2+3n5+n5

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Q: = Let f be a function defined for t≥ 0. Then the integral L{f(t)} . - fotº e- 0 provided that the…

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A: Given query is to find indicated derivative.

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A: Please see the below picture for detailed solution.

Q: Answer true or false. If L{f(t)} = F(s) and L{g(t)} = G(s), then ¹{F(s)G(s)} = f(t)g(t). O True…

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (et-e-t)² L{f(t)}…

A: Given function f(t)=(et-e-t)2  f(t)=e2t+e-2t-2×et×e-tf(t)=e2t+e-2t-2   Formula L(eat)=1s-aL(c)=cs

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Q: Fill in the blank. (Enter your answer in terms of t.) 1 e-{2}- L²s² + n²π² 2_2

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Q: Find the area between two curves f(x) = x² + 3x and g(x) = 6x.

A: The region bounded between the curves fx=x2+3x and gx=6x

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Q: Find V. (Fx G), if F(x, y, z) = 4xi+j+13yk and G(x, y, z) = xi + yj – zk. V. (Fx G) =

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Q: a) b) z c) 5√5 d) none 5√5 18. Find the ranges of values of x for which the curve y = x4 - 6x³ +…

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Q: #3 Test the exactness and solve the equation. (2xy 3x²)dx + (x² + y)dy = 0

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Q: Find the G.S. about xo = 0 for the following DE's (x²+4)y" + 2xy' - 12y = 0 1.

A: Please see the below pictures for detailed solution.

Q: Solve: y" + 4y = x² + ex Yc=C1+C2_ Type the letter corresponding to your answer. Yp=A A_____ B с = A…

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Q: f(x) = 2x^3 − 3x^2 − 18x − 8 Factor f(x) into linear factors. Don’t forget to include the leading…

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Q: Evaluate the surface integral s G(r) dA, G(r) = x+y+z, S: z=2x-y, 0 ≤ y ≤ 1, 0 ≤ x ≤ y

A: Given:    Gr=x+y+z,    S: z=2x-y       0≤y≤1, 0≤x≤y Substitute z=2x-y in Gr     Gr=x+y+2x-y…

Q: [xcsc (y/x) - y]dx + xdy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

A: The given differential equation is; [xcsc (y/x) - y]dx + xdy = 0

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Q: Find the equation for the slope of the tangent line to the curve below at any point (x,y). 2x + 5y =…

A: Given, 2x+5y=3y

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