Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

Q: Evaluate: ³²₁₂[z³(x + y)³] dz dy dx

A: Given, ∫-43∫-12∫01z3x+y3dzdydx

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: 3 .4 ²³₁₂₁ (4x²y — z³) dz dy dx

A:

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

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Q: Let F(x,y)=ln(x² + y2), then answer the following (1) Find the function's domain (2) Find the…

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Q: ¹₁1+x²x+2y dy dx

A: We need to evaluate the following iterated integral as following: ∫-11∫2x21+x2x+2ydy dx

Q: Given a second order differential equation dx 2x = e³t dt where t = 0, x = -5. Using Laplace…

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Q: Compute the average value of the following function over the region R. π f(x,y) = cos x cos y…

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Q: II. Find the inverse of each matrix. 5 -11 -9 1. -7 DO 8

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

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Q: Find the solution of the given initial value problem. ty+3y=t²t+5, y(1) = 2, t> 0 11

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Q: f(x) = x - 3, g(x) = x² Find (f + g)(x). 2 - (f + g)(x) = x+x-3 Find the domain of (f + g)(x).…

A: It is given that f(x) = x-3 g(x) = x2 We need to find the solution to the given questions.

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

A: Given data

Q: classify the following PDES :- 827 827 дхг 82z =X+Зу +2 буду дуг 2 2 X ох Иxx - 2xy Иху +Ў Иуу X •…

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Q: CSC X csc x - sin x - dx

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

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Q: Find the area of the region above the curve y=x²-6, below y=x, and above y=-x.

A: Let's find area of region.

Q: Q9. If W = f(u)=u' + sinu+Inu, and a=ax+by, where a, and b are constants, show that aw aw b. ax

A: We have to prove the given statement.

Q: 4. Evaluate the double integral: Y SZ (Hint: Change the order of integration to dy dx.) dx dy. +1…

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Q: 2 убличк In'/xl alx

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Q: -2 Evaluate: ²₁²[(x²-²²] 0 x+y du dt

A: Topic = Integration

Q: (3) If R is an integral domain has non zero characteristic, then Char(R)=..... (i) 5 (ii) 4 (iii)9

A: Option (i)

Q: 3 Evaluate: ₁ S 1²,₁ S² [(x²-x²)²] dx dy x+y

A: To evaluate the given double integral.∫-14∫03x2-y22x+y dx dy

Q: 2. Solve each of the following integrals using integration by part: a) √3x² In 2x dx b) 5x sin 3x dx

A: Integration is evaluated.

Q: 10) y7 exbx

A:

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: (x² - y²)²] 1²₁ 1² du du dt x+y Evaluate: ₁ S

A: Given ∫-13∫02x2-y22x+ydudt Since x2-y22x+y is constant with respective u and t, we take constant out…

Q: Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed…

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Q: Evaluate: ff xy² dx dy

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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: -3 -2 ²₁ ² [z³(x + y)³] dz dy dx

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Q: Evaluate: √₂²³ Sª₁ S₁ (4x² yz — ) dz dy dx -

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

Q: Evaluate the following Integral using integration by parts X CSC X S - dx CSCrCOU

A: Use by parts method of integration

Q: q-Sin ²1x1 1²/x/_alx

A:

Q: 1. The simple interest charged on a 60-day loan of Php 8,400.00 is Php 119. Find the simple interest…

A: Use simple interest formula

Q: Find the solution of the given initial value problem in explicit form. 7x y' = , y(0) = -9 y + x²y…

A: In this question, we will solve the given IVP.

Q: (2) Z/(5) =....... (i) (5) (ii) 5Z (iii) {[0],[1],[2],[3],[4]}

A: We have to find the operation

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

A: Follow the procedure given below.

Q: S77/2 Su² sin (=) dt du Evaluate the integral: f/2.

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Q: -2 -t² rln s Evaluate the integral: 5² 5²² n fote" du ds dt

A: We have to evaluate the integral ∫12∫tt2∫0ln st eu du ds dt.

Q: Evaluate the integral: -2е π/3 ƒºƒ²² ƒ”¹/³ t ln u tans ds du dt see

A: Given

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: answer

A: We will solve the problem.

Q: Let f : R 7−→ R be defined by f(x) = 2 − 5x. Show that f is bijective, and find f^(−1)(x).

A: Let f:R→R be defined by f(x) = 2 - 5x.

Q: please do the second (b)

A: Let's find volume when rotated about y axis.

Q: II. Find the inverse of each matrix. 5 -11 1. -7 -9

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

Q: Solve the boundry-Valued PDE 24 = 4 24 = 484 ठेप ulo,д) =8 ёру using the genval method -12X-39 ans:…

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Q: Find the particular solution of the DE y11 + 24y = 0 subject to the initial conditions y(0) = 2 and…

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Q: 1. Given vector 2 0-3 is 2. It is known that a à vector : ( 2 ) and 3 = (-1) is a vector in 1R³ with…

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