Express the integrand as a sum of partial fractions and evaluate the integral. 9 y 2 5 y-y-2 -dy = *** Express the integrand as a sum of partial fractions. y y²-y-2 (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Q: Find the values of x, y and that correspond to the critical point of the function: z = f(x, y) = 4x²…

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Q: Write an equation of the line containing the given point and parallel to the given line. Express…

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Q: 4. Find the exact arc length of the curve over the stated interval: x=3t², y=t³,0 ≤t≤2

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Q: 2. Find the derivative of the given function. (a) f(x) = tan²x. (b) g(x) = xsinx.

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Q: The joint density function for a pair of random variables X and Y is given. [cx(1 + y) f(x, y) if 0…

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Q: you have 2 . DU also can you do explain the integration by part showing what you are integrating

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Q: Consider the function f(x) = 4 2 x² x7 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then…

A: Topic = Integration

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: The concentration of the antibiotic in the bloodstream is modeled by the function C(t) = 6(e−0.4t −…

Q: A chemist has three different acid solutions. The first acid solution contains 15% acid, the second…

A: A chemist has three different acid solutions. The first acid solution contains 15% acid, the second…

Q: Using the ratio test to determine the convergence or divergence of the series series. Divergent The…

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Q: 5. Find the explicit solution of the given initial-value problem. dy e-x-ex dx 3+4y a) = y(0)=1 (b)…

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Q: Effect of Capital Expenditures on GDP An economist has determined that a certain country's gross…

A: Given function f( x ) = 620x15

Q: 8. Solve the following. (a) Find the equation of the tangent line to the graph of f(x) = x²-9 at x =…

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Q: 1

A: We have to simplify and write in x according to the given information.

Q: Find by implicit differentia dy dx xey = x - y

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Q: A lamina with constant density p(x, y) = p occupies the given region. Find the moments of inertia Ix…

A: Solution is given below:

Q: 4. Evaluate the limit, if it exists: lim x+1 a. 1 b. -1 x²-3x+2 x-1 c. d. 0 does not exist

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Q: G(x) = − 1x². +3 H (x) = − 1x² – 7 M (x) = − 1x² + 1/

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Q: Consider the function f(x) = 1−3x², -3 ≤ x ≤ 1. Use the derivatives to algebraically answer the…

A: Given, As per given question we need to find the extreme points of the function fx=1-3x2 on the…

Q: Calculate the derivative of the function. HINT [See Example 3.] h(x) = 3[(6x − 1)(x − 1)]−1/3

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Q: Use the graphs of f and g shown below to find the following: (a) g (f (2)) = (b) f (g (4)) EHH f(x)…

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Q: The domain of origin that satisfies the function f(x)= (x)/(x+2) is.

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Q: A farmer finds that if she plants 40 trees per acre, each tree will yield 20 bushels of fruit. She…

A: According to the given instruction, the answer is as follows

Q: Flow of Water from a Tank Water flows from a tank of constant cross-sectional area 40 ft² through an…

A: We have to find the rate of decrease of height.

Q: Consider the function f(x,y)=e^4x−x^2−4y−y^2. Find and classify all critical points of the…

A: Given function:- fx,y=e4x−x2−4y−y2

Q: For the given double integral, sketch the region of integration and write an equivalent double…

A: Given: I=∫1121∫y11ydxdy It means that the region bounded by the curves x=y, x=y11 from 0 to 121 is…

Q: Assume that it costs a company approximately C(x) = 800,000 + 360x + 0.0005x2 dollars to manufacture…

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

Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (4,…

A: To Find : Distance of point (4,6,3) from the plane x-y+2z=10

Q: (b) g(x) = (x + e*)², [0, In 4]

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Q: a = (0, 1, 2), 128. c= (1, 0, 1) - b = (-1,

A: Given: a=0,1,2b=-1,0,1c=1,0,-1

Q: Solve the equation for x given that 1 ≤ x ≤ 8: ln x = sin x, using 5 iterations of Newton's method.

A: To find the solution of the following equation ln x = sinx by using Newton's method For the…

Q: Find the general solution for the differential equation. dv 6- - 12xy - x = 0 y = = 1/2 + Ce=x² y =…

A: Given differential equation:- 6dydx-12xy-x=0

Q: 1 e) lim (-—-—-₂--²-4) x-3x-2

A: M=limx→3(1x-2-4x2-4)

Q: . Find the polar equations x-3y+2=0

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Q: Let f(x) = x4 lnx for all x > 0. I

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Q: Consider the ellipse 4x² + 2xy + 2y² = 88. (a) The derivative on this curve is dr dy = dx (b) Find…

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Q: Solve the differential equation. 2xy + 4x + (x² - 4) dy = 0 dx

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Q: Compute [5t³ - 8t + 1] d dt

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Q: Find and simplify the derivative of f(x) = ln(cosh (ax))

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Q: Find the length of the curve y=ln(1-x^2) for 0≤x≤1/8

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Q: X x+3 3x-1 Evaluate the limit, if it exists: lim a. 0 b. undefined C. co|w d. 1

A: Given : limx→3  x3x-1 To find: The value of given limit

Q: A chemist has three different acid solutions. The first acid solution contains 25% acid, the second…

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Q: let y = 5 log (x+1) find y'

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Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 4 meters per minute…

A: Need to find out the rate of changing of area outside the circle but inside the square changing.

Q: The Second Gate As you move through the first gate, you can see another gate not far in front of…

A: Given: g(x) = x+5x2-25 The function does not exist when their denominator is zero. That is,…

Q: Suppose that the position of a particle is given by f(t) = 5t³ +7t + 9. s = f(t)

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Q: Find the surface area for the portion of the surface z − 2x + y2 = 21 that lies above the triangle…

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Q: Solve the separable differential equation dx 1 x² + 25 dt and find the particular solution…

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Q: Find the derivative of the function. f(0) = cos(8²) f'(0) =

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Q: Find the general solution of the following reducible second-order differential equation. Assume x, y…

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…