f) y = x²-1 x²+x-2

Q: Using exact Solution, find the general solution of the following differential equation: (cos2y -…

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Q: 2 3) 9 = x ² sin x y વચ્ચે ઝ 4) y = sin x 1-2 cos x

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Q: 3 Evaluate: ³₂²₁¹ [2³(x + y)³] dz dy dx

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

Q: ³₂²₁²[z³(x + y)³] dz dy dx

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

A: Follow the procedure given below.

Q: (5) If f(x) =........, then f(x) is reducible in Z5 [x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x²…

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Q: -t √3u U Evaluate the integral: So So So S² S³ 2442 ds du dt s²+u²

A: A detailed solution is given below.

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

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Q: Evaluate the following * 6cos (2x) dx O3sin(2x)+C O 2sin(2x)+C O sin(2x)+C O-3sin(2x)+C

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Q: Z4 e: 2₁₁ (4x²yz - ) dz dy dx 1 4

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Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: Given : Let I be a proper ideal of the commutative ring R with identity. Then I is a _______ if and…

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

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Q: 22. Find a domain for the quantifiers in 3x3y(xy^ Vz((z=x) v (z = y))) such that this statement is…

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Q: derivative of (√2)^csc4x

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

A: Follow the procedure given below.

Q: 2 3 Evaluate: y cos(z5) dx dy dz 0

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Q: Evaluate: xy² dx dy

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Q: 3 Evaluate the integral: Soft²eu du dt

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Q: Consider the parametric curve: x = ln (8t) y = 5t³ Which integral gives the arc length of the curve…

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Q: The value of A. +3+2x² +C C = 1 + x² +2+C 20 [ (² + 3) *²x² dx B.+²+3x³ +C D. none of the answers

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Q: 6. Evaluate the line integral y²³ dr + ²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: In this question, we need to evaluate the given line integral.  The given vertices of rectangle are…

Q: Evaluate: ff xy² dx dy

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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: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) 9…

A: Follow the procedure given below.

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

A:

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: 1. 3 If the total cost function is given by TC = 300 +5q+ what is the marginal cost when q = 3? q² 1…

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Q: Find the point on the line y = 8x closest to the point (1,0). (Use symbolic notation and fractions…

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Q: 2. I. Evaluate each determinant. -4 3 -3 2

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Q: Solve the general solution of the following linear differential equation: (y-cos²x) dx + cosxdy = 0

A: Given (y-cos2x)dx+cosxdy=0To find general solution:

Q: Evaluate: xy² dx dy

A:

Q: Solve the given initial value problem. O x³y²y³ = -18 O x³y² + xy³ = -18 Oxy² + x³ = -18 O x¹y² + y²…

A: So,it is non exact differential equation.

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

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Q: Evaluate: ƒ³, ƒ²₁ √√₁²[z³(x + y)³] dz dy dx -3

A: Given :∫-33∫-12∫01z3x+y3dzdydx

Q: s s² s² sln teu du ds dt

A: We have to solve multiple integration.

Q: Evaluate the integral: ² ls teu du ds dt 0

A: We need to evaluate the following triple integral ∫12∫tt2∫0lnsteudu ds dt

Q: Find the area of the region bounded by the curves 1 y = (x+8)²¹ Y = 4 and the x-axis using vertical…

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

A:

Q: Evaluate: ₂₁(4x²y — z³) dz dy dx-

A: ∫03∫-24∫104x2y-z3dzdydx

Q: Write down a differential equation of the form = ay + b whose ay dt all other solutions diverge from…

A: Here, the differential equation is of the form  dydt=ay+b⇒dydt=ay+ba⇒dyy+ba=a dt⇒∫dyy+ba=∫a…

Q: Q1. The parametric equations of the lines L1, and L2 are given as: L: x=-2+1, y=3+2t, z=-t+4 L₂:…

A: Let's find distance between two lines.

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: Consider a continuous function f(x) = 2e-1-2x, which is true about the relative extrema of f? f has…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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

A: To evaluate: ∫π2π∫0tsin(4t-u) du dt

Q: Find the volume of the solid that results when the region enclosed by y = √√√x, y = 0, and x = 49 is…

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Q: 5x 2 Evaluate: f²f3³xdz dy dx 0 2

A: Here is the solution:

Q: 3 .4 ²³₁₂₁ (4x²y — z³) dz dy dx

A:

Q: 2. The function below, and its graph, gives the rainfall in mm/day that falls in the month of May,…

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Q: Evaluate the line integral y dx + xy dy where C' is the rectangle with vertices (0,0), (5,0), (5,4),…

A: