The form of the partial fraction decomposition of a rational function is given below. A B = Now evaluate the indefinite integral. [ 8- (3x² + 25x) (x + 5) (x²+4) 8 (3x² + 25x) (x + 5) (x²+4) dx = A x + 5 + Bx + C x² + C = +C

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Q: Solve for the general solution: 01--0.9+ Cel20/30) 01-0.9+ Cel-20/30 OI--0.9+ Cel-2/300) O1-0.9+…

A: To solve the given differential equation

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A: To find the limit of the piecewise function

Q: 2. Find the absolute maximum and minimum of f(x) = 3x³9x² +5 on the interval [0, 4].

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Q: Problem 6e. Practice. Find the Derivative of the following function: F(x)= C08 (2x) Le-Sin (2x)…

A: Given query is to find th derivative.

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Q: 2. Determine whether the series (a) Converges 00 (b) 5 3/2 converges or diverges. Diverges

A: need to find out the the series converges or diverges.

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A: We will find the curve length as shown below

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A: We can find the solution of the given differential equation by using the variable separable method.

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Q: 1) Evaluate ]] where D = {(x,y) | y≤x≤1, 0≤y≤1} and [ dy fe²de dx Also explain why they're the same.…

A: Please see the below picture for detailed solution.

Q: Condense log(x-1)+log(x+2)=1

A: Solution:

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Q: The graph of the derivative of f(x) is shown below: 7+ 6 5 4 3 2 -7 -6 -5 #4 -3 -2 -1 -1 -2 -3 -4 -5…

A: Topic = Functions

Q: How many x-intercepts would the function shown below have? f(x) = (x² − 5)

A: given that,   f(x)=x2-5   how many x-intercepts would the function have?

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Q: Find the volume of the solid that lies above the cone p= 12 cos(p). 1 3 and below the sphere

A: Given:- Cone ϕ=π3 Sphere ρ=12cosϕ

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A: Given function:- fx=x3+6x2-96x+19

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A: Please see the below picture for detailed solution.

Q: W (2) = 3z +9 2-z

A: The given function is: Wz=3z+92-z Use the Quotient rule: fg'=f'·g-g'·fg2 And the Power law:…

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A: Given query is to find the derivative of the expression.

Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y (a) 256 (c)…

A: Topic = Area

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Q: PS #1 9. A ladder 10 ft long rests against a vertical wall. Let 0: angle between the top of the…

A: A ladder 10 ft long rests against a vertical wall.Let θ: angle between the top of the ladder and the…

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A: The given function fx=9x2+x3+20+24x We have to find the absolute maximum and absolute minimum values…

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Q: For the demand equation, use implicit differentiation to find dx p² + p + 9x = 120

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Q: Please

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Q: 80. A cubic function is a polynomial of degree 3; that is, it has the form f(x) = ax³ + bx² + cx +…

A: f(x) = ax3+bx2+ cx + d on differentiating,   f '(x) = 3ax2 + 2bx +c which is a quadratic in x and…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation r(t) =…

A: To determine the domain of the given function

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Q: b) y = 2x + 5

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Q: Find the divergence of the vector field F. F(x, y, z) = In(7x²+ 8y²)i + 56xyj + In(8y² + 3z²)k F(x,…

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Q: (a) lim 2²/ I→∞

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: f(x) -5 0 Let F (x) be the anti-derivative of f (x) such that F (6) = 15. Then F (0) is O-1 0 1 0 10…

A: Given query is to find the value of F(0).