By direct partial integration, Solve the following PDES 8- 82u = COSX COSYSXUCX,t) Ex u(π, y) = 2 coss 2 2 axdy 2 Ans: u(x, y) = sinx siny + x² + 2 cosy - #2² サ An ♥

Q: 1. Let R be the region in the first quadrant enclosed between the circles x² + y² = 9 and x² + y² =…

A: x= rxos(theta) y= rsin(theta)

Q: S- tanh e cosh(z) – sinh(z) -dz

A: Let's evaluate given integral.

Q: (x + 2)" Q4. Find the convergence interval and radius of the series : Σ (-1)**² n=l n

A: We need to find interval and radius of convergence.

Q: و و ۹۷۶) (0) لا او A 2 1 - X Jx (x+2 - 4

A: This is a problem related to differentiation. Based on the general formula and concept we will…

Q: 4 nd the area of the region bounded by 2x = y²+1 nd the y-axis using the horizontal strip.

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Q: Find the transition points. y = 3x6 - 27x4 (Use symbolic notation and fractions where needed. Give…

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Q: 6. The value of A. sin ¹¹x + √1 + x² + C B. sin-¹ x - √1 + x² +C C. sin-¹ x + √√1- x² +C D. sin…

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Q: Differentiate the function. P(w) = 2w² - 6w + 4 W

A: Given function is differentiated.

Q: on The radius of the sphere is decreasing at a rate of 2in/min. What is the rate of change of its…

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Q: Show that (x+2)² = ln(x + 2) - x+2 + C.

A: Topic = Integration

Q: Water is flowing into a conical vessel 18cm deep and having a diameter of 10cm across the top. If…

A: We have to find the rate of volume.

Q: Determine the exact length of the polar curve r 3 sin for 0≤0 ≤T. =

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Q: Q3 A) Write the first five terms of the following: - 2. {1- (-1)") (3n+2 B) Determine which of the…

A: "since you have asked multiple question,we will solve first question for you.If you want any…

Q: Evaluate the integral by making the given substitution. (Remember to use absolute values where…

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Q: Determine y = Yc+yp using Non-homogenous equations: Method of Undetermined Coefficients Given: y" +…

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Q: show that V(x, y) = x 'f (2x+y) is the general Solution of av X du 2X 1 = V ду dax

A: Explanation of the answer is as follows

Q: II. Find the inverse of each matrix. -9 6 2. 4 -8

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Q: Evaluate the integral: 7/20¹² sin (1) dt du

A: Follow the procedure given below.

Q: What is the answer? Show your complete answer (with a graph) in a given-required-solution

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Q: Find the area of the region bounded by the curves 1 y=; y = = 4 and the x-axis using vertical strip.…

A: Let's find area of the region bounded by curves and given line y=4.

Q: Solve the given differential equation. All solutions should be found. dy 3x²-8y- y³ 8x + 3xy² dx…

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Q: The value of sin cos (x²+)+C C. cos (x²+)+C xp B. -cos (x²+)+C D. -cos (x²+)+C

A: Topic = Integration Correct option = B

Q: 5x 3 2 Evaluate: ffxf²dz dy dx 2

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 1. Find the distance between p(-2, 3,0) and Q(2,1,5). 2. Find the direction of A = 2i - 3j+7k. 3.…

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Q: 3 -2 Evaluate: ₂₁ [2³(x + y)³] dz dy dx

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Q: - 2.f(x,y) = y²x¹ey.

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Flag question Evaluate: ³²₁ [2³(x + y)³] dz dy dx

A: Let's evaluate given triple integral.

Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ į, y = = 4 and the x-axis using…

A: Explanation of the answer is as follows

Q: I. 1.) Simplify. Write "undefined" for expressions that are undefined. 2 [164] -6 -5

A: Topic = Matrix

Q: Evaluate the following * [x√x² - 7dx

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Q: Evaluate the integral: S/2 So sin(4t-u) du dt

A: To find the integral , ∫π/2π∫0t  sin(4t-u) du dt

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

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Q: Use the table of integrals to evaluate the integral. 2 √2²47x²³ √4x²-x+ d² dx

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Q: Determine the roots of y"" - 4y" + 3y = 0

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Q: Find the solution of the given initial value problem. ty' +4y=t²-t+7, y(1) = 4, t>0 y =

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Q: Evaluate: ƒ³₁ ƒ²₁ √√²[z³(x + y)³] dz dy dx

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Q: (x²-y²)²1 Evaluate: ₁²² du du dt x+y

A:

Q: The value of A.cos(x²+)+C cos (x² + + C fx sin (x²+3) de dx B. - cos (x² + 5) + C D. -cos (x²+)+C

A: Option (B)

Q: Find the area of the region above the curve y = x^2 - 6, below y = x, and above y = − x.

A: Given region bounded above by  y=x2-6  and y=-x  and bounded below by y=x

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 13x)y², y(0) : =…

A: Given,dydx=(1-13x)y2                     y(0)=-16

Q: Evaluate the following √ (2²2 + + 6x − 1)²(x + 3)dx (x²+6x-1)-5 + C 2 (x²+6x-1)-5 3 +C (x²+6x - 1)5…

A: We have to solve given integration.

Q: Solve the general solution of the following Linear differential equation: y' = x - 2xy

A: Let us consider a differential equation of the form, dydx+P(x)y=Q(x) So its integrating factor is…

Q: Which of the following functions will be continuous on (0, 3)? OA. h() = 12 8² + 6| OB. g() = 7/2-16…

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Q: Evaluate the integral: S/2 sin(4t - u) du dt

A: The integration of the double integral is Sin(4t-u), u from 0 to t, t from pi/2 to pi.

Q: Evaluate: xy² dx dy S

A: Given: ∫04∫0yxy2dxdy

Q: 7) y = exz 8) y = 3 x ²

A:

Q: Evaluate: ƒ²₁ ³² ²₁ 0 [(x²-y²)²] x+y du de

A: Follow the procedure given below.

Q: Solve the given differential equation. All solutions should be found. (5y¹ + 2x³y) dx − (4xy³ + x¹)…

A: Using integrating factor make equation exact

Q: Q1 Solve the following differential equations. 1. (x + 1) = x(y² + 1) dy dx

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Q: Evaluate: ₁ [2³(x + y)³] dz dy dx

A: Please see the answer below.