Question 20 Let f(x) =cos(3x) & g(x) = e . Which of the following is true. (f+ g)(x) = 2 e2x + 3sin(3x) dx f(g(x)) = -6sin(3e2X) e2x dx (x) = - 2sin(3x)cos(3x) dx (fg)(x) = e2Xcos(3x) - 3e2*sin(3x) dx

Q: QUESTION 7 Evaluate 3x5 3x4+6x³-3x² - 6x x²-2x-In O x²-4x 2 O x²-4x 2 O rẻ-2r 2 [(x-1) 1/6(x+2) 16/3…

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Q: Question 19 Let F(x) -1. √1+t¹ dt for x in (-∞0, ∞o). Find F'(- 5 sin z O F'(x) = -√1 + cos²x O…

A:

Q: 7x Cos + COS cos 2.

A: According to trignometry formula:cos a +cos b =2cosa+b2 cosa-b2Given,cosx2+ cos7x2a=x2; b=7x2

Q: Question 2 Find the value of f(z) = z3 +z as z-i along the paths (a) parallel to the x-axis coming…

A: Given  f(z)  =  z3+ z To evaluate the limit of f as z → i  along two different paths

Q: Question 7 Find the partial derivative of z with respect to x 8: da = -2x (3x²+1) sin(x²) + 6xcos…

A:

Q: Question 9 The integral - dx (x²+4)² can be transformed to which of the following when trigonometric…

A: The given  integral can be transformed to which of the following when trigonometric substitution…

Q: Question 12 If the solution to e2x sec2(e2x+1)dx is equal to ktan (e2x+') + C, find the exact val S…

A:

Q: Question 11 xdx=2 2 xp- 2 2 A) True B) False Question 12 To evaluate e"sin2(e2") cos(e2") dx. we let…

A: Find your answer below

Q: Evaluate in terms of gamma function: x°e-3¤ dx O r(7) Or(17) O(7) OI(7)

A:

Q: 32 Question * (3 Points) The proper transformation for sin²x to make the f sin²x dx readily…

A: substitution

Q: Question 4 When x°cos (x²)dx is evaluated using IBP, the value of J v du is? A B -cos (x2) cos (x2)…

A: We need to choose correct option.

Q: Question 25 of 34 Evaluate f (x²-16)² dx +3 O A)I DON'T KNOW B) NONE OF THESE OC) (x-16)-6…

A: It can be solved by the use of substitution and reduction formula .

Q: Question 17 Evaluate D3(sinx – 4e) (A) -sin x-32е2х B sin x-32ex -cos x-32 e2x D cos x-32 e?x

A: Solution

Q: Question 2: Find the solution of the given DE (2xy cos(x?) – 2xy + 1)dx – (sin (x²) – x²)dy = 0

A: The given question is taken from the calculus in which we have to find the solution of the given…

Q: Problem 3. Show that the function cos(n²r) f(x) = 2n n=1 is differentiable on [0, 1] and f'(x) is…

A:

Q: Question 2 d cos x Find dx In x A. X sin x x In x sin x+cos x x (In x) 1 COs X x In x sin x+cos x D.…

A: To find differentiation  ddxcosxlnx

Q: Question 003: Complete the following question involving Substitution Method. Given the integral S8…

A: Given : ∫8sin3x-7cos3x-75dx

Q: Question 6 The following DE sin(x) +y cos(x) =1 can be written as dx cosx) dy 1-y xp sin(x) None of…

A: topic - differential equations answer is none of these

Q: Question 1. Find the general solution of the following ODE: y" – 4y' + 3y = -6e² + 40 sin z.

A:

Q: Question 3 If f(x) = f A sec ³x 1+elanx B 1+tan²x 1+etanx In (secx) √ 1+tan²x C tanx 1 + e sec²x D…

A:

Q: Repeat Problem 109 for g(x) = cos2 x.

A: g(x) = cos2x

Q: f (0. 80108) = sin 3 (0. 80108) + cos 2 (0. 80108) – (0. 80108)²

A: Given,

Q: Question 2 Find the solution to the Bernoulli Equation. (3siny - 5x) dx + 2x²cotydy=0

A:

Q: Question3: A. Find the general solution of the following first-order ODE xy' = y + 2x³ sin² (²)

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Q: 450 400 AA 350 300 250 200 150 100 50 -4 -50 8 16 24 28 36 12 20 32 -100 -150 -200 -250 -300 Dy =…

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Q: Question 16 Evaluate: [Vx + sin/ dx. A None of the given choices 2x+ cos/x B + C 2 © x+2cosx + C D…

A: As we know that; The sum rule: ∫fx±gxdx=∫fxdx±∫gxdx And ∫a·fxdx=a·∫fxdx, where a is the constant.…

Q: Question 20 sin (x) Evaluate: dx sin(x) +1 1- sin(x) (A) cos(x) +x+C 1+ sin(x) B cos(x) -- x+C cos…

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Q: QUESTION 16 Let f(x) = sin(x) -e*, Po=0, and p, 1, then by Secant method P2 = 0.657614 0.678614…

A: Given that: f(x)=sinx-e-x,       p0=0 and p1=1

Q: 1.4 = 0.9062 x Cos (1-√³x) dx = 0-6034 How?

A:

Q: Question 5 Does x2 – 10 = x x sin x have a real solution? Show your process. %3D

A: yes the equation have real solution

Q: Question 2 Differentiate the following functions (i) If y= e-t sin 4t, prove that +6+2y = 0. (ii)…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU AS PER…

Q: Problem 2. Consider the following sequence of functions fn (x) = r" sin(nr), r€ [0,1/2], n =…

A:

Q: In 1 & 2 find dz/dx by the chain rule and also by rewriting z. 2 = (3x) z = /1- cos?x 1. 2.

A: Let's find.

Q: QUESTION 4 SIn(x +2) dx = O A (x +2) In(x+2)- 20x +C O B. x In(x + 2) 20 " -x+ C 20 OC (x +2) In(x…

A: Integrated by part

Q: a 0.9062 Cos (1-√3x) dx = 1/2/2 : -0-1 a=0.5968

A:

Q: QUESTION 3 Je* sin(3x)dx = %3D e8x OA 73 (3 sin3x – 8 cos3x) + C e° 8x OB. (8 sin3x – 3 cos 3x) + C…

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Q: 2. 3. ત્ર 6 -1 cos²2x dx X - dx

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Q: Question 2. Find the largest interval of existence and uniqueness of solution for the IVP 1 tx" +…

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Q: Question 6 Differentiate: y = arccot (x) + arctan 2 + x 1 - 2x 0 1 (E) None of these O:2x O 1-2x

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Q: (1/2 3. x coS TX d Jo

A: Consider the given integral, ∫012xcosπxdx To solve the integral, apply the By-part rule of…

Q: Question 6 Find the general solution of (2x + y cos (xy))dx + x cos (xy) dy= 0 Show your solutions…

A:

Q: QUESTION 11 Scos(x) dx Find 1 sin(x) – sin (x) + ar 3 1 cos(x) + cos (x)+ C O 1 sin (x)- 3sin2(x) +…

A:

Q: Question 1 d dx Jx & S" cos(t) dt = O a) cos (x2) · 2x b) cos (x²) · 2 O c) sin (x²) d) sin (t² ) e)…

A: topic - integration and derivatives

Q: Problem 1  Verify that  (1/((x^2)-1))=(1/2)[(1/(x-1))-(1/(1/(x+1)) And use this equation to evaluate…

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Q: Question 170 Calculate f 3 in x.cos x dx. (a) 3sin x cos x , In 3 (b) 3cosx . In 3 (c) 3sin x. In 3…

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Q: Question 11 Integrate f 9z2 - 5+dz Type only the numeric value below and be sure to show all of your…

A:

Q: Question 11 Зсos3x-1 To evaluate f scos - dx, the integrand can be transformed to 1-sin?x A.)…

A: We put 1-sin2x=cos2x and then solve it. Follow 2nd step.

Q: ∫√(1+2sin3x) (cos3x)dx

A:

Q: Problem 7. Let f(x) = -2x* cos(x) f'(x) =| %3D

A: The answer is

Q: Activity 6: Find the first and the second derivative of the following: 1. у 3D е cos x 2. y = sin³…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…