Find the exact length of the curve. y = In(1-x), 0sxs 8.

Q: In the integral, cos?tsin2tat , the correct u using general power formula is; A cost B sin(2t) © sin...

A: Given integral is ∫cos2tsin2tdt =  ∫cos2t(2sintcost)dt = 2∫cos3tsintdt Now taking u = cost  Differen...

Q: x²-x+1 -dx. Evaluate:

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Q: 5. Find the maximum area of an isosceles triangle whose perimeter is 18 inches.

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Q: `In²(Ine*) dx (A) Inx B In'x Inx2 D Ine" None

A: integration

Q: Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that...

A: This is a limit, continuity and differentiability problem

Q: Suppose that f(z, y) = x°y?. Find the directional derivative of f(x, y) in the directional (1, – 1) ...

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Q: What is the value of (3+2i)³ + (3- 2i)6

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Q: x2-x+1 -dx Evaluate: A 2,2-2,2-2,24C

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Q: If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x). %3D r...

A: here f(1)=2,g(1)=1,f(5)=3,g(5)=2 Lets find f'(1),g'(1),f'(5),g'(5): for 0≤x≤2 f'(x)=∆f∆x=4-02-0=42=2...

Q: In the integral, Jcos?tsin2tdt , the correct u using general power formula is;

A: We are asked to find the integral  

Q: cose Evaluate the integral: de. 4- sin?e A None of the given choices -sn(글sne)+c В © sin (ano)-c sin...

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. + 2)3/2, 2 < y <...

A: To find the exact area of the surface

Q: If Mesin(2x) dx= eSin(2x) + C_then the M is equal to Blank 1 (use small letter, no spa

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Q: Match the function on the left to its appropriate antiderivative on the right. Prompts Submitted Ans...

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Q: Question 21 Evaluate: J(3x + 1) d. S(3x+1)°d_

A: ∫3x+12dx

Q: 2-x+1 -dx .

A: Please refer attached file for solution below

Q: 3 [f(x)dx=+C, then f (x) : A True (B) False

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Q: Solve the following (i) |10 - 3x |  ≤ 17  (ii) x² - 6x ≥ 13

A: We have to solve the inequality

Q: Let u and v be functions of x. Then J (u-v)dx is equal to ux – vx +C dx

A: Topic-:- integration

Q: sin(t) Find the equation of the tangent line to f(t) = 9 +9 cos(t) at t = 3 (Use symbolic notation a...

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Q: - ydx + (x++ xy )dy = 0

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Q: In-(Ine") dx A Inx 8 In'x © Inr? Ine E) None

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Q: '8х — 16dx 3D2 :- 2 dx

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Q: A function F (x) is called an antiderivative of a function f (x), if A F(x)=f (x) F(x)=f (x) F (x) =...

A: Let's find. 

Q: dx In then the integrand is the same as 4+e¬* 4e*+1 (А) True B False

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Q: Which of the following indefinite integrals willresult to logarithmic expre. • Inx. A Ssec-(3x) dx 2...

A: We will find the solution. 

Q: A solution of a differential equation which cannot be generated by specializing the parameters (arbi...

A: To find out the correct option. 

Q: If two functions F & G are both antiderivatives of the function f , the F (x) =G(x). (A) True B Fals...

A: We need to explain that given statement is true or false.

Q: Let {an} be a sequence of non-negative numbers. Suppose that the sequence {a,} converges to 0. Show ...

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Q: 5e2*dx ,4x – 6e2 + 1 | 3e 2r B 3e2 – 2 (c) 3e2x – 1 D 9e x – 6e 2* + 1 E) None A)

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Q: cose Evaluate the integral: de. 4- sin2e

A: Follow the procedure given below.

Q: Question 1 The coefficient of Sec(x) when J (tan(x) – sec(x))*dx was evaluated is Blank 1 (use numbe...

A: Explained below 

Q: 1. y' = e-" (2x – 4) y(5) = 0 2. dy = by°r y (1) = dz 1 25

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Q: 3 Find the Taylor Series of sinnx centered at 0.5 and x = 5

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Q: Cost C(q) = 86 + 0.13q - 0.007q2 + 0.0009q3. (a) Find C'(100). Interpret C'(100). O This is the rate...

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Q: Use the definition of the derivative (long method/ increment method) to find the derivative of the f...

A: We will find the derivatives. 

Q: / In(sin(x)) dv using simple substitution, dv =f (x) dx_ Determine the valut of f(x) if In order to ...

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Q: Evaluate: | tan(4x + 3)dx i -In |cos (4x+3)|+C A COS 4 В 4 - In |sin (4x + 3)|+C In |csc (4x+3)|+C D...

A: Given: ∫tan(4x+3)dx =∫sin(4x+3)cos(4x+3)dx Substitute : cos(4x+3)=td(cos(4x+3))=-4sin(4x+3)dx=dtdx=-...

Q: Mesin(2x) dx = eSin(2x) + C, then the M is equal to B %3D

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Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves...

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Q: Question 11 dx 4+e A 4+e- B) 4e+1 E None Question 12 sin'ydy 1+ cosy A 1+cosy B 1- cosy siny sin'y

A: NOTE:- AS POSTED MULTIPLE QUESTION, WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU AS PER BARTLEBY GUI...

Q: Sv 8x – 16 dx=2 x- 2dx A True B False

A: Show that,∫8x-163dx=2∫x-23dxAnswer:-4LHS=∫8x-163dxLet 8x-16=udifferentiate8dx=duTherefore LHS=∫u38du...

Q: Question 5 When you evaluate dr. The sum of the coefficient of x" for any constant n>0 is Blank 1 (u...

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Q: (Inºx– 3lnx) +dx (A Inx B Inºx © Intx D In x- 3lnx E In x- 3 (F) None

A: The integral is  ∫ln6x-3lnx4xdx

Q: Which of the following integration expression can be transformed into integral of power (Choose 2) 5...

A: Solved below

Q: x-e -2r -dx x²+e-2« *2(x-e-2«) A x²+e-2r xp- – 2(x-e-2x) dx x2+e-2r B -2x 2+e =21 dx x²+e-2¢ /2(x?+e...

A:

Q: cose Evaluate the integral: de. V4- sin?e (A) None of the given choices -sn(글sne)+c B (ane) e -1 sin...

A: The solution is given in the next step.

Q: S (sin(Inx?)) 3 -dx? Which of the following is equivalent to the integrand of

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Q: Evaluate the integral

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Q: In( sin(x))dv using simple substitution, dv =f (x)dx_Determine the valut of /(x) if In order to eval...

A: The given integral is: I=∫lnsin x dv