1. Consider a point in Cartesian coordinates given by (3√//3, -3,-8). (a) Find a corresponding cylindrical coordinates. (b) Find a corresponding spherical coordinates.

Q: Given the hyperbola 2² - 4y² + 2x +32y-27= 0. Find the vertices of the hyperbola. O a. NONE OF THESE…

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Q: 2. Using your calculator, determine how many solutions the system has. Then without a calculator,…

A: This question is based on solution of Polar function.

Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

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Q: 2. For a given perimeter, what is the ratio of the length to the width of a rectangle that will have…

A: Solve the following

Q: Find the derivative of the following using the differentiation rules. (x²-2x) (In x³-3 tan x) x√x y

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Q: 4. (a) Find (b) Hence evaluate d dx √1+x² X S (1+x²)³/2 dx.

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Q: What is r 1- O Option 1 2 2 sin 0-3 cos 0 3 y = ² x + 1 2 x² + y² = 2y²-3x Option 3 in Cartesian…

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Q: Which of the following integrals represents the area inside the curve r = 3 + 2 cos 0 and outside…

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Q: W (4) Find Laplace Transform F(s) for the variable x or y in the equations a- +2y'-3y=32e³;…

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Q: W (4) Find Laplace Transform F(s) for the variable x or y in the equations a- y" +2y'-3y=32e³; y'(0)…

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Q: integrate * Se³x+2 dx 2017 O +C d (2) 200 (14(14(1))) STOPISTOP!

A: The integration of the integral is e3x+2.

Q: Choose among the following suitable to define the given integrations: * f(x + 1) sinx dx Not…

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Q: The value of x for which the series - OA25x<3 or 3<x≤ 4. OBx<2 or 4<x. OC. None of the choices in…

A: We will solve this question by first calculating the radius of convergence of the series.

Q: INSTRUCTION: Please box your final answer. Find the Laplace transform of the following: 1. y" + 2y'…

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Q: Given the function f(x, y, z) = x ln(1 − z) + following and simplify your answers. a) | fx b) u fxz…

A: We can answer both the answer as below

Q: Which of the following describes the partial fraction decomposition of a rational function of the…

A: When there is a whole square in the denominator, it it divided into two parts. One consisting of…

Q: day dx5 + day dx4 - 6 d³ y = 0 dx³

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Q: Find a Maclaurin series for f(x) = x2 e–x giving the first four nonzero terms and the general term.

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Q: x² In solving for the antiderivative of f(x)= √√4-x² using trigonometric substitution, f(x) dx is…

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Q: Evaluate the following integrals (a) 2x+3x-2 dx

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

Q: tex Given; ·S= dx 2 Applying rationalizing substitution, find dx in terms of z. (2 z + z) dz A z² z…

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Q: dx dx.

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Q: Select all statements which are TRUE. For statements with cross products, assume the vectors are in…

A: Let's find.

Q: y=x² - 4x and y=−x² + 2x.

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Q: 5 3 +-6-0 dx 4 dx 3 dx 2x - 3x a.y = (C₁ + C₂ + С₂)e* + С²e²x + С¸è¯ С_e 2 5 2 2x -3x b.y = C₁ + C₂x…

A: We have to find the solution of  d5y/dx5 +d4y/dx4 - 6d3y/dx3=0 This is a homogenous 5th order…

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. The x-coordinate of the centroid of the…

A: We first sketch the given region using a graphing calculator.  We will consider the graphs about…

Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. Then Arearegion = [₁ f(x) dx + f[ g(x) dx,…

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Q: If R is the disc with center at the origin and radius 5 then the numerical value of [xdA is equal to

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion= = ["5(x) f(x) dx + dx +…

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Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³ +1| + C dx…

A: Given

Q: Determine the area bounded by the curves x^3 - y = 0 and y + 3x^2 - 4 = 0, using a vertical element.…

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Q: 1/2 Scave [ (a²-x² - x²) ¹²h dx (8) = √5 (9² - x²)³/²2 [³ (a²-x²) ¹1²2 0/² ] + c 15

A: Given:       ∫a2x6-x8dx Rewrite:      =∫x3a2-x2dx substitute u=a2-x2→dudx=-2x→dx=-12xdu…

Q: Which among the equation represents for equating the coefficient of x^2 form 3x + 2 = (A+B+C) x^2 +…

A: Given  =&gt;3x+2=(A+B+C)x^2+(-A+B-2C)x+(-2A) =&gt;(A+B+C)x^2+(-A+B-2C)x+(-2A)-3x-2=0…

Q: Estimate the value of 217(1/3) a. approximation b. differentials

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Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

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Q: Consider the following differential equation: dy : 2xy² dx i. Use the method of separation of…

A: using method of separation

Q: Given the function f(x, y, z) = x ln(1 - z) + and simplify your answers. a) fa b) fxz sin(x - 1) 2y…

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Q: 9 Calculate the expression. Show the solutions. Use the calculator for checking only. 【(XY)¹ - Z)¹…

A: Topic:- matrix algebra

Q: The integral can be rewritten as 6u³ (a). u + 1 6u4 (c). u² + 1 :). -du du dx 3³√x + √√x 派 派 6u² u²…

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Q: The value of x for which the series Σ- O A. x<2 or 4<x. OB.2<x<3 or 3<x≤4. OC.2<x<4. O D. 2<x<3 or…

A: Given

Q: The face of the gate of a dam is in the shape of an isosceles triangle 4-m wide at the top and 3-m…

A: I am attaching image so that you understand each and every step.

Q: Use the shell method to find the volume of the solids generated by revolving the shaded region about…

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Q: U= at ² w + 0х2 8² w dy² where 61, 62, 63 are constants and b₁ +6₂ +63 " 8² w + = W. az² Item 8.pdf…

A: Topic:- application of partial derivatives

Q: Solve the following boundary value problem using finite difference method given that…

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Q: The directional derivative of f(x,y,z) = In 1+yz from P to Q(-1,-1,2) is given by .... .(Correct to…

A: Given :f(x,y,z)=lnx21+yz-3xz2

Q: 4x8 Evaluate efv dx 2 Use rationalizing substitution. A e√e² -2 -2√2 Arctan = √√e² - 2 + C e* 4 (B)…

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Q: dx Evaluate ·S= using rationalizing substitution. x1/2 + x2/3 (A) none of the choices B 6 In (x1/6)…

A: The integration of the integral is  1/(x1/2+x1/3).

Q: Part II: Point Conversions 1. Convert (2,7) into a rectangular coordinate. 2. Convert (4,-4) into a…

A: I am attaching image so that you understand each and every step.

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 4x + 8y = 8,…

A: Given: 4x+8y=8, y=0 x-axis, x=0 y-axis So, the bounded region is as shown below. Apply the disk…

Q: Pls

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