Find the volume of the region bounded above by the sphere x² + y² + z² = 2 and below by the parabo- loid z = x² + y².

Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: 5x 2 Evaluate: ²3x²dz dy dx 2

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

Q: What is y' of y = sin¹ (cos x)? O A. y' = ATHE sin + 1-cos² 1 O B. y' = 1 OC. y'= sin z 1-cos² z OD.…

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

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Q: Evaluate: ₁³₂₁(4x²y — z³) dz dy dx -2

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

Q: Evaluate: ³₂(4x²y - 2³) dz dy dx

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Q: CSC X csc x - sin x - dx

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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: Evaluate: ff xy² dx dy

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Q: √3 3-x² √√3√ √√3-x²√1 4-x²-y² 1 dzdydx

A: Explanation of the answer is as follows

Q: S- tanh e cosh(z) – sinh(z) -dz

A: Let's evaluate given integral.

Q: What are the first 5 terms of the sequence represented by a=2n-3a n "n-1, where a₁ = 4₂

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

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Q: What is the direction of the vector (8, -7)? A 41.19° B 138.81° с 221.19° D 318.81°

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Q: Find the area of the surface obtained by rotating the curve y = cos(2x), 0≤ x ≤ π/6, about the…

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

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Q: +∞ (x²+4)3/2 dx

A: To find: Integration

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

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Q: Determine the intervals on which the function is concave up or down and find the points of…

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

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Q: 3 f²f²² ²³ y cos(z³) dx dy dz 0

A: The given integral:∫01∫0z2∫03ycosz5dx dy dz

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: 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: ๆ ³₁₂₁ (4x²y — z³) dz dy dx -2 J1

A:

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: 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: Find the general solution of (d²s)/(dt²) + 2(ds/dt) + 5s = 0. OA.y = C₁e(t) cos2t + C2 e(t) sin3t…

A: Let's solve given diffrential equation.

Q: Evaluate the integral: -2e π/3 ₁²/³ tlnu tans ds du dt

A: Topic = Integration

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

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

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Q: If g is said to be the antiderivative of the function f then O a. Inconclusive O b. O c. O d. g'(x)…

A: Here we have to choose the correct option.

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: 3x(xy - 2)dx + (x³ + 2y)dy = 0; f(1)=2 Find the positive root of y at x=2. Use 2 decimal places.

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Q: 2. Evaluate all of the integrals. a. [² sec²rtan r (1+sec x)² dz

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Q: Evaluate: ff xy² dx dy

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Q: Evaluate: ₁ [2³(x + y)³] dz dy dx

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Q: Question 1 Express the Laplace Transform of the following functions: (a) f(t) = 2e5t sinh(7t) — t8…

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Q: Evaluate the following * [csc² cot (5x+6)/2 + C cot(5x+6)/ 5+ C - cot(5x+6)/ 5+ C cot(5x-6)/ 5+ C…

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Q: Using the Mean Value Theorem, given f(x) = x³, what is/are the value of c, where 0 < c < 2 such that…

A: Topic = Functions

Q: Find a number in [0, 1] such that the difference of one third the number from its cube is minimized.…

A: Let the number be x. Let f(x)= x³-x/3 So, f'(x)= 3x²-1/3

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: dy Write down a differential equation of the form dx 17 all other solutions diverge from y = as t →…

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Q: VSDE of tan xdx + y * cos^2 ((x) * dy) = 0

A: (Sinx/cosx)dx+ycos²xdy=0 (Sinx/cosx)dx=-ycos²xdy (Sinx/cos³x)dx=-ydy tanx sec²xdx+ydy=0 Integrate…

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

A: Topic = Integration

Q: Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis and…

A: Given problem is :

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: For each of the following ,find fx fy fxx fy fyx and fxy f(x, y) = x cos+ ye*. 2.f(x,y) = y²x¹e². 3.…

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

A: Given data

Q: 2x-1 Q7. Find the convergence interval and radius of the series : 2 (-1)" . Σ(-) 2n-1 n=1

A: