Using Long (Euclidean) division then decomposition into partial fractions x4 – 4x2 – x – 3 | dx х2 — 2х— 3 - - is equal to Inlx – 3| +Inlx – 1| x3 + + x2 + 3x + C 3 none of them the above In|x + 3| +In|x + 1| Inlx – 3| + Inlx + 1| x3 +x? + 3x + C 3 x3 +3+x + 3x + C the above the above *Inlx – 3| + In|x + 1| x3 + + x2 + 3x + C 3 the above

Q: Since log,(a) = c → a = b°, 1--2 In(즉)- e-1/2. » X = So, y' = 4x(1 + 2 In = 0 when x = -1/2 and y" =…

A: Since logba=c→a=bc                          1=-2lnx5  ⇒-12=lnx5  ⇒e-12=x5⇒5e-12=x⇒        x=5e-12

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A: ∫e3x-e-2x-e-x4dx=∫…

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Q: Find the general solution 1. (D² – D – 2)y = 0 2. (D² + 3D)y = 0 3. (D2 – 5D) + 4y = 0 4. (D² – 9)y…

A: 1. D2-D-2y=02. D2+3Dy=03. D2-5D+4y=0 Note:    Multiple sub parts are given, we are answer only three…

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A: Given query is to find the equation of the tangent at x = 1.

Q: dx 2. Find the integral x²(x+1) In (***) + C b. In (***) - +C 1+ C c. In (***) ++ c d. None of the…

A: Here we have to find the integral

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Q: dy + 2ху dx %3D

A: integrating factor method.

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Q: y = 3x - x2 and y = 2x 11 %3D

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Q: d,x+7 3. dx 2x-3

A: To find: ddxx+72x-3

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A: see below the answer and explanation

Q: b. S 2*³-4x²-x-3 dx х2-2х-3

A: First we divide the polynomial  using long division

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Q: Which type of discontinuity does the function exhibit at x = 3? -x2 + 1, -1 sx <0 2х, f(x) = { -4,…

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Q: Of the Sollds gene by Volving the regions Doundeu by graphs of equation given iines. y = 3x2 y = 0 X…

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A: The domain of a vector valued  function r(t) = f(t) i + g(t) j + h(t) k  is the set of all possible…

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Q: S- x³dx is equivalent Vx²-4 Using trigonometric substitution,

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Q: Using appropriate substitution 1 dx V9x² – 36x + 37 Is equal to

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Q: 3. Evaluate the integral 7/4 1 + cos²0 do cos²0

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Q: 4y" – 4y' + y = 16e*/2

A: Find your answer below

Q: 1) Use a double integral to find the area of the region enclosed by y= x² and y = 2x.

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Q: Find the quotient of the complex numbers. Leave your answer in polar form. co cos

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Q: 2) Use polar coordinates to evaluate ff, sin OdA with R being the region in the first quadrant…

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Q: An antiderivative for is: 22 +81+20 1 O In + C I+8 ㅇ 올tan-1 () +C 금i미플의 O In 28|+ C O tsec- (4) + C

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Q: e?y - dy (ve)" – 1

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Q: Repeated Imaginary Roots of Auxiliary Equations Solve the equations: 4) (D3 + 36D)²y = 0 5) (D3 +…

A: The given differential equation,4. D3+36D2y=05. D3+1002y=0

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = t'i+ t°j K(t)

A: The given formula is; κt=r't×r''tr't3 And rt=t2i+t9j

Q: A general solution of the differential equation d3y/dx3-3d2y/dx2+4=0

A: The given differential equation,        d3ydx3-3d2ydx2+4=0

Q: Product/Quotient/Chain Rules for Differentiation: Answer the following

A: Differentiation

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: ydx — хdу %3D у?dy

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Q: I. Find the derivatives of the following 1. f(x) = 2x2 + 3x - 7 %3D

A: We know that ddxxn = nxn-1               and                    ddxpxn = p ddxxn = p× nxn-1 = pnxn-1

Q: 3.) (x* - x? + 6) (8x + 4x)dx Note: You are not allowed to use The Method of…

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Q: The following table gives the sunrise and sunset times for various dates of the year in Lincroft,…

A: Note: There are multiple questions. Few questions has multiple subparts.No specific question has…