a. The volume of R using cylindrical coordinates with dV = r dz dr de where R: 0 ≤ x ≤ 2,0 ≤ y ≤ √4 = x²,0 ≤ z ≤ √√4 − (x² + y²). Draw the solid R.

Q: Q6. Let W = f(r,0), r = 0 = tan"'(y/x), find aw Ох > and ди ду in terms of r and 0.

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Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A: Above question is solved.

Q: y ye 2x+4 tax

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Q: - x, then answer the following (1) Find the function's domain (2) Find the function's range. (3)…

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

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

A: Topic = Matrix

Q: The function f(x, y) = x² + y² √x² + y² +1-1' (a) {(x, y) = (0,0)} (b) {(x,y) = R²2} 2 if : (x, y) =…

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Q: Solve for x the following inequality and show their solution set {x: x2-x-30≤0}

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Q: Let R be the region enclosed by the polar curve r (0) = 1 + 2 cos² (0) where 0 ≤ 0 ≤ Y R 1 Which…

A: Consider the region R

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: 7. Compute the area of the region R enclosed by the curves y = x² - 1 and y = 1- x.

A: We have to find out the area

Q: Find the volume of the region bounded above by the sphere x² + y² + z² = 2 and below by the parabo-…

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Q: Let R be the region enclosed by the polar curve r(0) = 20 sin(0) where Y X R 1- 1 Which integral…

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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: 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: 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: Find g'(x) for each of the following functions. 4) g(x) = sin(u²)du 5) g(x)=₁*Inu du

A: Solution: The objective is to find the derivatives of given functions

Q: I. 4. Evaluate each determinant. 2 -5 2 -1 4

A: We have to find out determinant

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

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Q: Obtain the general solution of the given differential equation: tanydy = sin3xdx

A: The given differential equations tan2y dy=sin3x dx⇒sec2y-1 dy=143sinx-sin3x dx    As…

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

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

A: This is a problem related to function and number system of the function. Based on the general…

Q: Evaluate each determinant.

A: A = -1523

Q: Given m = 6, n = 1, and v = ⟨–4, 7⟩, what is v(n –m)? Show your work for full credit.

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Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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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: Consider the following quadratic function. g(x)=3x² - 6x-4 (a) Write the equation in the form g(x) =…

A: This question can be solved using the concept of general equation of parabola.

Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: Obtain the general solution of the given differential equation: dy = cos²xcosydx

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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: Find the general Solution of the following PDES • з Их + 2 Иу , u(x,c) = чех (3У-2х)12 ans3- исх, у)…

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Q: 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator which is…

A: Given that, A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator…

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

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Q: For the following exercises, use the second derivative test to identify any critical points and…

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Q: 3 So So t : t² etu du dt

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Q: f(x, y) = = /25 - (x - 2)² - y²

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Q: A В D ľ КIN 5л 2 (2 — 4sin(0) + 2 sin²(0)) d0 (2 - 4 sin(0) + 2 sin²(0)) d0 (1 — 2 sin(0) + sin²(0))…

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Q: let f(x)=x2 -9y  and  g(x)= √x. find the domain of (f o g)(x) and h(x)= 1 / (f o g)(x)

A: Let f(x)=x2 -9x and g(x)= √x. Now,        (f o g)(x)=fx                =x2-9x                =x-9x…

Q: 3. of the solid enclosed by the hyperboloid z = Set-up the iterated double integral in polar…

A: Given

Q: the graphs of y=2x^2 and y=mx -2 intersect at the points A and B. The point B has coordinates (2,8),…

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Q: 2 убличк In'/xl alx

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

A: First, we find ∂v/∂x and ∂v/∂y  and substitute them in the given equation, if it satisfies the…

Q: I. 7. Evaluate each determinant. -3 4 -5 2 -3 -5 1 3 5

A: To evaluate the determinant -34-52-3-5135

Q: √ (2x - 7)6 12 (2x + 7)- 12 (2x - 7)5 + C + C (2x - 7)-6 12 (2x + 7)6 12 - + C - + C

A: Topic = Integration

Q: strip.

A: y-axis using the horizontal strip ,  y = 0 , x = 4/0+1 , x=4  so y-axis at x=4 and y= 0. Area of…

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

A:

Q: Find the area of the region enclosed by the curves y =

A: answer is in next  step

Q: (d) lim 1-x-x² x-∞ 2x³ - 3x + 1

A: In this question, we want to evaluate the limit of the given expression.

Q: Solve the given differential equation. All solutions should be found. dy x³-8y dx x NOTE: Use c for…

A: The given first-order differential equation is: dydx=x3-8yx⇒dydx=x2-8xy⇒dydx+8xy=x2...(1)