b. √ ( 3 √ √x + ²) a dx

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Q: ∞ n=1 (n+1)(3² − 1)¹ 32n

A: As per our guidelines we only solve one question and rest of the question will be reposted.

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A: Indefinite integral

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Q: 0 3. Evaluate the definite integrals: (a) CS Scanned with CamScanner² (x² – 3x) dx (b) 5 1 √I -d.x

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Q: Consider the function f that is continuous on the interval [-5, 5] and for which ff(x) dx = 4.…

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Q: 4 2 + Find the area of the portion of the Sphere x² + y² +2²= 9 between the planes Z=1 and 2 = 0.…

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Q: Question You work at a farm that wants to build three identical rectangular corrals in a row against…

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Q: Decide whether the integral is improper. [ In(x²) dx proper O improper Explain your reasoning.…

A: Here we have to decide whether the given integral is improper.

Q: Sketch the region R and evaluate the iterated integral ff- (1-4x+6y) dy dx y -1.0 O -0.5 3 -1 xn-[…

A: The given integral is  ∫01∫02(1-4x+6y) dy dx re write the integral: ∫01∫02(1-4x+6y) dy dx =∫01…

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Q: x +4 x²+2x+5 1₁ da

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A: We want to find the volume of revolution on  about the y-axis

Q: Solve the differential equation below using series methods. y’’ — 4xy' — y = 0, y(0) = 4, y'(0) = 2…

A: Here, the given DE is: y''-4xy'-y=0    ...(1) with y(0)=4,y'(0)=2

Q: (b) D₂f = 2 cos(xy + 2z) Dzzf = -4 sin(xy + 2z) Dzzyf = -4x cos(xy + 2z)

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Q: Use the second derivative test to find the location of all local extrema in the interval (2) for the…

A: We can solve as follows

Q: 1. An undamped spring-mass system with mass m = 2 and a spring constant k = 8 is suddenly set in…

A: Solution in step 2

Q: The f2e4t sec2e4t dt is {A} = = tan e 4t + C {B} = sec³e4t + C 16 {C} /e4t tan e4t + C {D} et…

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Q: Problem 1: Obtain ODE by eliminating arbitrary constant A, B, and C y = Ae2x + Be + C

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A: Given: y=2x3-6x2+3x

Q: Seatwork: Obtain the general solution of the following differential equations 1. (xy² + x) dx + (x²y…

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Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. a. So f(x) dx…

A: Let's find.

Q: using least cost method

A: The total cost using least cost method is Rs 284

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Q: 1. What rule is applied in the following given? * Dx (-13) = 0 Power Rule of Differentiation Product…

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Q: 0 if t 5 Find the Laplace transform, F(s) of f(t) F(s) = ķ

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Q: Evaluate the iterated integral. 17 [₁₁/₁² (x² + y²) dx dy = i 17 LL" (2² + y²) dx dy

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Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

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A: answer is in next step

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Q: the slope intercept equation of a line that passes through (0,-6) and (3,-4) is

A: Given points are (0,-6) and (3,-4)and here (0,-6) is (x1,y1) and (3,-4) is (x2,y2)We know the slope…