A solid is formed in the first octant bounded by the plane z = 6 - x - y and the cylinder 4 - x². Using dxdy as the order of integra- tion, SET-UP the double integral that will give the volume of the solid on the right. Y = X z=6-x-y 6. 4 2 y=4-x² y 4

Q: Determine the general solution of y" - y = 0 given y₁(x) = e e-2x using reduction of order

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Q: By direct partial integration, Solve the following PDES 8- 82u = COSX COSYSXUCX,t) Ex u(π, y) = 2…

A: Given ; del2u/delx del y=cosxcosy.

Q: Q5/ Solve for x the following inequality and show their solution set (x: x2-x-300)

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Q: The value of A. sin-¹ x +√1+ x² + C B. sin ¹x-√√1 + x² + C C. sin-¹ x + √1- x² + C D. sin¹x-√1- x² +…

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

A: The given differential equation is: y'''-3y''-y'+3y=0   So, we can also write as; D3-3D2-D+3y=0

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: S- tanh e cosh(z) – sinh(z) -dz

A: Let's evaluate given integral.

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

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Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: 2 убличк In'/xl alx

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Q: dy Solve the differential equation. X dx = y + x³ + 3x² -2 x

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Q: 3 Find the area of the region bounded by 2x = y² +1 and the y-axis using the horizontal strip.

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Q: Evaluate: ³₂(4x²y — z³) dz dy dx

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

A: Let's find area of region bounded by given curve and y axis.

Q: Find the slope of the tangent to the curve y = 3e^(2x) at (0,3)  a. 3  b. 2  c. 6  d. 12

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Q: Let R be the region in the first quadrant bounded above by the parabola y = 4 x² and below by the…

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

Q: identify any extrema of the function by recognizing its given form or its form after completing the…

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

A: Follow the procedure given below.

Q: зи Evaluate the integral: So So So u s2 +u2 ds du dt

A: Given: I=∫02∫0t∫03uus2+u2dsdudt   As we know the common integral. ∫11+x2dx=tan-1x+C

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: 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: NO PARKING See Se THIS BLOCK 2AM 5AM STREET ARLING 2 HOUR PARKING THIS BLOCK 9AM 6PM EXCEPT SUNDAYS…

A: Solution

Q: -2 Evaluate the integral: ² ft² n s teu du ds dt

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Q: I. 2.) Simplify. Write "undefined" for expressions that are undefined. 5 3 2 I(1J + -6 -6 2 0 2

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Q: The Substitution Method states that A. If F'(x) = f(x), then [ ƒ (u(x))u²(x) dx = F(u(x)) + C B. If…

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Q: 6. I. Evaluate each determinant. тут 3-3 4 1 0-1 -1 -4

A: Given data

Q: 1. Show the drawing and entire solutions to know the differential equations of the lines' families…

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

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

A: Given: I=∫-23∫-12∫01z3x+y3dzdydx   As we know the Power Rule: ∫ax+bndx=ax+bn+1an+1+C, where a &…

Q: 3 Evaluate: ³₁₂₁(4x²y — z³) dz dy dx

A: Topic = Integration

Q: Evaluate: du [(x²-y²)²1 ³₁ 1² du dt x+y

A: Given , ∫-13∫02x2-y22x+ydudt

Q: The utility function of a certain good is given by U(x) = 60x - x2 where x represents the number of…

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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.…

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Q: from the date set, find the value of f(7) by use lagrang method X 3 6 9 11 y 12 13 14 16

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Q: 1. Solve the following Linear Systems of Equations by Gaussian Elimination: 2.) 3x + 3z = 0 2x +2y =…

A: On solving this we will get

Q: Evaluate the integral: So So So 2 rt c√3u 0 0 น s²+u² ds du dt

A: Given problem:-

Q: 2. Express the iterated integral as a double integral in polar coordinates. 1 X 1 Lo dy dx 16/2 x² +…

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Q: Differentiate the function. h(t) = √√t - 7et -6 (F) h'(t) = -7e² =-- (1) t

A: The given function is: ht=t7-7et   As we know that; The Sum/Difference Rule: f±g'=f'±g' The Power…

Q: t√√t + ,2 + t dx

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Q: Three forces with magnitudes of 5 pounds, 8 pounds, and 120 pounds and direction angles of 90°,…

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Q: CSC X csc x - sin x - dx

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

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Q: +00 0 x (x²+4)3/2 dx

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Q: ๆ ³₁₂₁ (4x²y — z³) dz dy dx -2 J1

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Q: Evaluate: ²₁²²-²² du (x²-y²)²] S du dt x+y

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Q: Evaluate: £²³₁ £²₁ ¹²[z³(x + y)³] dz dy dx

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

A: Follow the procedure given below.

Q: Let R be the region enclosed by the polar curve r (0) = 3 ln (0) where 7π <O< 8 Y X 72 ㅠ R 1 1

A: Given Curve rθ=3ln(θ)whereπ2≤θ≤7π8

Q: A stone, projected vertically upward with initial velocity 112 ft/sec, moves according to 8 = 112t -…

A: We have to choose correct option

Q: 1. Find the Inverse Laplace Transforms of the following. 4) 48-60√s s4

A: A detailed solution is given below.

Q: Evaluate the following * S sin(4x) dx O cos(4x)/4+C -4cos(4x) + C O-cos(4x)/4 + C O-4cos(4x) + C

A: We can find the answer as below.