2.2 INTEGRATION OF RATIONAL FRACTIONS 16

Q: Evaluate and Solve the function using the product and quotient rule of differentiation. Show your…

A: Here we have to use the concept of derivatives.

Q: P af af Q3.If f(x,y)=sin(x-3y) + sin(x) find: and əy ax

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Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

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Q: Find y dy ·S- using the substitution +5= √√y+2 U /y+2 /y+2−5) (5√√y+2+y+24) + C…

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Q: 18dx ·S (4x² +9) 19.

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Q: S₁ 2 63 Evaluate: A 16 B 105 C) None 16″ D 105 2π E 63 sinxcos³xdx is equal to

A: We can find the integration as below

Q: 18. f(tan 2x + cot 2x)² dx

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Q: QUESTION 18 Determine the third order MacLaurin's polynomial for f(x) = ex.

A: Kindly note that I have authority to answer only one question. If you want remaining question to be…

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: We need to setup integral.

Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

A:

Q: The integral O [se Ss S S sec²0 de 1+ tane sece tane de sece - 1 O x dx x²+√√x²-1-1 sine de 1+ cose…

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Q: Read, analyze and solve for the following. Express your answers as decimals rounded off to two…

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Q: dx S= can be transformed to which of the following when trigonometric substitution is used (x²+4)²…

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Q: 50 50 ["*" (ax² + hx² + cx) dx = 2b ["* x² dx -50 0 (A) True (B) False

A: As we know that; The Sum Rule; ∫fx±gxdx=∫fxdx±∫gxdx And ∫a·fxdx=a·∫fxdx  where a is constant.   We…

Q: 11. 5 [ese xdx

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Q: Evaluate S= 3x5 3x4+6x33x2 - 6x + In O x-2 2 x² - 4x 2 O x² - 4x + In 2 x²-2x-In + In -dx using…

A: Given problem:-

Q: Use the table to the right to find the given derivative. d[ f(x) dx x + 7 X = 5 = (Simplify your…

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Q: 4. Find the domain of the following functions: 10 (a) H(x, y, z)= 1+x² + y² +4z² (b) K(w, x, y,…

A: A detailed solution is given below.

Q: Directions: Find the area of the region bounded by the curves. Use a clean sheet of paper for your…

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Q: 16. dx x√√16+x²

A: To find out the integration.

Q: 2. Let f(x) = 3 cos 2x + sinx. a) b) Show that f'(x) = -5 sin 2x. π 3π In the interval <x< one…

A: We need to find derivative and normal.

Q: How do you multiply cube in an equation?

A: Solution

Q: QUESTION 9 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)…

A: Please see the below picture for detailed solution.

Q: Find the general solution of the ODE. d'y dy +3. dx² dx Stre

A: Given d2ydx2+3dydx=5x+xex

Q: QUESTION 14 I 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x==…

A: Find area between two curve

Q: Evaluation. 1. f5x³-³ dx √x3 Determine the antiderivative for each. Show complete solution. 2.…

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Q: Evaluate the following integrals/limit/s: 1. S√16-x²dx

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Q: dx e* + e* +ex 5. ・ So =

A: We can find the answer as below.

Q: S²- 16-x2 A 2 B) 8 0 None 4 E dx is equal to

A: I am attaching image so that you understand each and every step. Option "C" is correct answer.

Q: 6. ၂ 3z+1 -4) -dz

A: ∫3z+1(z2-4)2dzExpand:=∫3z(z2-4)2+1(z2-4)2dz=3∫z(z2-4)2dz+∫1(z2-4)2dzNow solving…

Q: x 0 Can also be displayed as: f(x) = [x - 1 when x < 0, 1 when x = = 0, x² 1 when x ≥ 0] For this…

A: The given function,     fx=x-1,x&lt;01,x=0x2-1,x&gt;0

Q: S₁ A B If 2x²+x-2 (x+1)(x²+1) ² 1 -- 2 U NIG 5 —— D E) None + -S₂ -dx = A x + 1 + B (2x) + C x²+1…

A: Partial fraction decomposition

Q: y dy Find S √y+2 A(√3+2-5) (5√3+2+y+24) + C B (√y+2-5) (5√/y+2¬y+24) + C 3 Ⓒ²(√x+2-5)(-3√x+2+y+21) +…

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Q: A 38. Which of the following equations is the correct representation of the perimeter (P) of the…

A: Given:  38) Norman Window:

Q: y dy Find ·S- √y+2 03 (√x+2-5)(-5√/y+2+y+21) + C ○ ² (√y+2−5)(5√/y+2+y+24) +C 3 (√√y+2-5)…

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Q: The volume of the solid generated by revolving the region bounded by x2-4y and y2 = 4x about b using…

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Q: 5 dx Evaluate: (x-3)² 1 A B C D E -1 ∞o (does not exist) 1 0 None

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Q: If " (x+5) dx = 14, then the value of b is equal to A) None B 2 (C) 4 D -3 (E) 3

A: Given

Q: Let S be the solid of integration of the given integral Q. (1.) Sketch S and label its boundaries.…

A: Given

Q: The position of a particle moving along the z-axis is given by s(t) = 3t2 +5. Use difference…

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Q: What is the value of f(1) - 16B in fx³ Inx dx = f(x) ((1/4) Inx-B) + C? (A) 2 B 3 C 0 D 1

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Q: π 5π Find the area bounded by the trigonometric curves y=sinx and y=cosx from x== to x== 4 4 (A)…

A: The region bounded by the curves y=sinx and y=cosx from x=π4 to x=5π4

Q: dx √2+√x −1 14. f-

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Q: f(x)=(6x¹-2x+1)

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Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: Being carefule to allow for parts of the curve being both above and below the x‐axis, to determine…

Q: Read, analyze and solve for the following. Express your answers as decimals rounded off to two…

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Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1) (A) 1/2 B)…

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Q: 3x5 3x4+6x33x2 - 6x (x-1) 1/6(x+2) 16/3 + In x+1 (x-1) 1/6(x+2) 16/3- (x+1) 1/2 (x-1) 1/6(x+2) 16/3-…

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Q: (a) An archaeological artifact is found to have 45% of its original carbon-14. How old is the…

A: Half life and decay

Q: /= 0 sin√xcos√x X Зл A 256 Зл B 512 3 C 256 D) None 3 E 512 -dx is equal to

A: