J I+ sin(x) sin(x) xp. Evaluate: 1– sin(x) A -2x+C cos(x) 2( sin (x) – 1] cos(x) B -x+C 4cos(x) + C sin(x) s(x (*) +C x+ cos D x- cos(x

Q: 32. y" + y = sec x; y = c1 cos x + c2 sin x + x sin x + (cos x) In(cos x), (-7/2, T/2)

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Q: Sco The value of cos (x+3) dx with U=x+3 is -cos (x+3) sin(x+3) +C -cos(x)+c

A: The given integral is ∫cosx+3dx.

Q: |(4e + 5z* – 3 sin z)dx- O 4e² – x³ +3 cos x + c O 4e? +x³ +3 cos x + c O 4e² +x³ - 3 sin a + c O…

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Q: Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 1/4 3/8

A: We have given  ∫x sinx cosx =fx sin2x-gx cos2x+C Let,  I=∫x sinx cosx dx I=∫x sin2x2dx I=12∫x sin2x…

Q: f(x)% 3D cos (x) -1

A: For a function f(x)=A cos(ωx+b)+c The amplitude of the function is |A| and the phase shift is b.

Q: Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 3/8 1/4

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Q: 8 sin x Find an antiderivative F(x) of the function f(x) such that F (0) = 1- 3 + cos r

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Q: Use integration by parts to evaluate 2x cos (x) dx -x?cos (x) +c - 2x cos (x) + 2sin(x) +c x?sin (x)…

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Q: f'(x)= 3cos(x)+5sin(x), f(0) = 9 a. f(x)= – 3sin(x)– 4cos(x)+7 O b. f(x)=3sin(x)+4cos(x)+11 O c.…

A: Topic = Integration Correct answer  = C

Q: a) f(x) = 3x + 5; interval [1,2]; %3D W = 10 interval ; 11m- b) f(x) = sin x;` %3D W = -1 2' 2

A: To verify the IVT for the specified function f, the interval a, b, and the indicated value w.a…

Q: 17. Derive A) f(x) = 10x* –- 32x + e² %3D B) y = e-* sin x

A:

Q: ). y² = 4x, 2x - y = 12 ). y = In x³, y = In x, x = e ):y = 2sin x, y = sin x from x = – to x : %3D…

A: As per bartleby guidelines for more than one part only first part is to be answered , please upload…

Q: Evaluate D(sinx – 4e2) D³(sinx cos x-32 e В -cos x-32e2 C) -sin x-32 e2x (D sin x-32 ex A

A: The objective is to evaluate, D3sinx-4e2x

Q: r 3n 4 Evaluate sin'x · cos'x dx 5. n /2

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Q: (a) f(x) = - x x – x² 4 (b) f(x) = 3sin(2x) + cos(6) (c) f(x) = sin(3) – 2³ + 4 %3D

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Q: x sin (x²) cos(x²), from a = 0 to b = x 2

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Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

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Q: 22. Find (i) f xe-x* dx (ii) Evaluate lx - 3| dx (iii) Use the substitution x 2(1 + cos 0) to show…

A: These integrals are based on substitution method. The solution is explained in the steps below.

Q: Evaluate f 3xV1 – 2x² dx A(1 – 2x*) + C B. (1 – 2x*) +c (1-2x²)³ D. +C 2 Evaluate S dx csc 2x-cot 2x…

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Q: ecot x 20. J sin² x(e- cotx) ax is equal to A. ecot x 1 + C ecot x C. -ecot x + C D. –ecot x + C

A: Given problem:-

Q: At what points (x, y) in the plane are the functions in Exercises 31–33 continuous?

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Q: f (x) = 5e"r³ tan(x) а. b. g(x): re cos(x) h(x) = sec(sin(/x)) с.

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Q: d) f(x) – e) f(x) = sin [In (x² - 3x)] sin x f(x) = 1+COS X

A:

Q: sin(x³ + y* ) Q3. Find of for the functions: .(x.y) (0,0) x'+y f(x.y) = .(x.y) = (0,0)

A: f(x,y)=sin(x3+y2)x2+y2 uv'=vu'-uv'v2

Q: -(sin³(x) + sin (x³) ) dx A 3sin'x + cos (x³) B 3sin?rcos(x³) + 3xr?cos(x³) © 3sin?x + cos (3x²) D…

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Q: Using FPI, find a critical point of the function: f(x) = x2 – 2e* cos x With an initial guess, xo…

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Q: 15. Evaluate f e sin2x cos 2x dx A. 2ecos 2x + C C. 2e sin 2x В. + C 2ecos 2x D. 2esin 2x + C

A: You need to have the idea how to use substitution in integration.

Q: Vx + sin/x dx. Evaluate: None of the given choices в x- 2cos/x +C 2x+ cos/x + C D x+2cos/x +C 2x-…

A: Let's find.

Q: 1. Consider [x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? A. 3/8…

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Q: (-1)° x*1 (2k –1)! 2k-1 k=0 a) sin x b) cosx c) sin x- x d) cosx-1 e) e* ||

A: Given,

Q: cos(x) dx = dx. Use - 0o (1+x²)² o cos(x) 00 cos (x) Compute Jo 1+x²)² dx. Note that 2 (1+x2)2 the…

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Q: dx 3. Evaluate: S V(x+2)(3-x) A. sin-1 (*) + 3x- C.V6 +x – x² -In |x-+v6 + x – x² |+C B. sin-1 (*)-…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 12. Evaluate ((1– cos x) dx a.) 1- sin x +C b.)x - cos x +C c.) 1- cos x+C d.) x- sin x+C 13.…

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Q: 8. sin x Find an antiderivative F(x) of the function f(x) = such that F(0) = 1. 14+ cos x

A:

Q: 9. The value of f 1-x 1+x A. sin ¹¹x + √1 + B. sin¹x - √1 + dx x² + C x² + C C. sin ¹¹x + √1- x² + C…

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Q: y2) = Br* -cos x. %3D A. 24x2 B. 24x + sin x+2 Given h(x) = -sec²x, determine the general…

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Q: Find (f −1)'(a). f(x) = 4x3 + 5 sin x + 2 cos x,    a = 2   (f −1)'(a) =

A: Consider the function f(x) =4x3+5sinx+2cosx.Compute the derivative of the given function as follows

Q: Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 3/8 1/4…

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Q: y" + y' = cos x + 4 e-* 1 y - C, cos x + Cz sin x +(sin x- x)- 4x e y = C, cos x + C2 sin x - x cos…

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Q: Sræsin(x³/2)dx= cos(x3/2) + C A 2 B) -을 cos(x3/2) +C ©-3/2 cos(x3/2 ++ C) C 2 D /xcos(x³/2) + C

A: Given: Let I=∫x sinx32 dx To Find: To evaluate the given integral.

Q: al f(x)= 2 sin (x – 3) – 1 To f(x)%3D2 2 b) f(x)=-6 cos (x + 1) + 3 T 1)+3 c) f(x)=2 tan (x – 1)+2

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Q: O 1:0: d (sin-x?) = (sin-1; dx 1 d V1 - x² dr (x²) خيار 4 1 V1- x4 2x V1-x2

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Q: 5. y + 4y= sin x + 3 cos x Ans: y = C₁+C₂ cos 2x + C3 sin 2x + sin x x-co COS X

A: To solve the given differential equation.y'''+4y'=sin x+3 cos x

Q: J (sin 3x)² = sin 3x xp- sin 3x CO = sin 3x xp- sin 3x On simplifying further, y2 (x) = cq sin 3x /…

A: In this question , constant is to be included in the last solution of the differential equation.…

Q: 2ク • *ý-4xý +6y =-X sinx 3 2. Ans y= C,X +C2 X+X Ssinx

A: We have to find the solution of the give second order differential equation

Q: y for the function f(x)= cos [x*sin (x²+1)] =, CoS 1/2 %3D ..…

A: The given function is fx=cos3x3sin12x2+1. Obtain the derivative as follows.

Q: x1'=2x1 + 2x2 + t x2'=-x1 + 2x2 + sint  x1(0)=1 ve x2(0)=1 sistemini çözünüz

A:

Q: Evaluate D°(cos x+e-2*) (A - cos x +64e -2x B - sin x – 32e -2 cos x – 32e-2 D sin x +64e -2x

A: Explained below

Q: 9. y"+y= sec² x Ans. y= c, sin x + c2 cos x0 + (sin x ) In(sec x+ tan x)–1

A: Let's find.