Evaluate the following integral using partial fraction decomposition. S 12 (x-4)(x+8) 12 (x-4)(x+8) S dx dx = =

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Q: Find the general solution of the given differential equation. 6  dy dx + 42y = 7 1.Give the largest…

A: Solution is given below:

Q: Finally, determine (x³. - x + 8) and simplify the result. Recall that multiplication is commutative…

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Q: - ƒ(x) = (x² + 3x) (x−¹ − x¯4)

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A: Please see the below picture for detailed solution.

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Q: Find two positive numbers satisfying the given requirements. The product is 1200 and the sum of the…

A: Let the number be x and y Given: xy = 1200 To find x, y for which x + 3y is minimum

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A: Given,Differential Equation y'y=sin2x.tan2x…

Q: 66. 1 - 1 2 + 2 4 68. + 5 25 1 4 + T 8 125 +

A: Question no. 66 & 68 solved

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Q: h) R = 3qe 9

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A: The equation for decay is:Pt=P0ektwhere t=time in years, P0 is the initial mass.

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Q: What else do you observe? Concept Check: Evaluate the following integrals: ·S 4. 5sin2x cos2x dx…

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Q: Give the appropriate form of the partial fraction decomposition for the following function. 3x…

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Q: Step 2 Now write the derivative in terms of x by recalling that u = x³ = x + 8. [eu] = (eu) du dx…

A: I have solved step by step in detail....go through the solution

Q: Question 29 Given 3x7 +825 - 21. determine, y' 630x +480x² + O 2520z³ +960x O 840x³ +360 P DE 126…

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Q: Let / be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

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Q: ive the appropriate form of the partial fraction decomposition for the following function. 9x² +7…

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A: The given function is f(x,y)=x4-5xy3+6y5 We have to find the fxx(x,y) and fxy(x,y)

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Q: Find {f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) cos( +…

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Q: Let f(x) = -6x4√√x + f'(x) = -2 x³√√x

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Q: 9 8- 7 16 1 A 3 يها 2 1 If f(x) f'(3) = = g(x) g(x) h(x)' 2 3 x-values then 5 4 يها 2 1 h(x) 1 2 3…

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Q: Find the derivative of y = 3x² − 2x + dy = 6x 2 dx dy dx dy dx Oy = = 3x - 1 = 3x - 2 6x - 2

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Q: 4. Find an equation of the tangent plane to the surface xy + yz+zx = 3 at the point (1,1,1).

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