48. Multiple Choice Find y" if y = x sin x. (A) -x sin x (B) x cos x + sin x (C) -x sin x + 2 cos x (D) x sin x (E) -sin 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: [1+sin x) 'cos x dx (sin x)4 +C A ) x+ sin x + B -(1+ sin x)*+C (sin x)4 -+C 4 sin x +

A: Substitute, 1 + sin(x) = t

Q: Evaluate the integrals

A: We have to evaluate the given integrals .

Q: 1. y = sin(x) tan(x) 2. y = cos (x) 3. y = cos(tan(x)) 4. y = tan(x) A. y' = -3 cos (x) tan(x) В. у…

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Q: Evaluate sin(x+y)-cos(x+y)=1

A: Given: sinx+y-cosx+y=1 Dividing both sides by 2, we get  12sinx+y-12cosx+y=12

Q: Evaluate cos x+ 2 cos x+1 dx sin x sin x - 3 cos x cost x 7. +x+c 2 cos x +x+c 3 cos X- cos x (sin x…

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Q: 3. y" +y = 2 cos x - sin x; y = x sin x+ x cos x

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Q: 1. y = 3 sin x – 4 cos x 2. y = x³ tan x 3. f(x) = cos x 1+sinx 4. y = csc x cot x f(x) cin?

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Q: { 1/(x + 2) , x2 , sin(x – 1)/(x - 1) , x 1. y = F(x) =

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Q: y" + y = 2 cos x – 2 sin x; y=x sin x + x cos x y" +y = sec x; y = x sin x + (cos x)In(cos .x)

A: We have two methods two check whether given function is solution of differential equation or not  i)…

Q: 5. ( sin (7x) cos'(x) dx sin'(x) dx 6. /2 7. cos'0 de 8. Jo sin (20) de

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Q: 3 The range of y = sin x is _______. -1 < x < 1 -1 < y < 1 y ≥ 0 y ≤ 0

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Q: 5) 5) g(x, y) = x²y + cos(y) + y sin(x) r(x, y) = ln(x + y)

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Q: ſcos (x/2) cos (x/3) dx * 3/5 sin(x/6) + 3 sin(5x/6) + C None of the choices 3/5 sin(5x/6) + 3…

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Q: 18. y'= (x+ycos x)/(1+ sin x) 2 = (x- 1)(1+ sin x) ( tan x +tan x 3 2 sec® x) +c.

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Q: cos x cos y y (0) = 0 sin x sin y - sin x cos y - y

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Q: 21. (1 + cos x)y' = sin x(sin x + sin x cos x – y). ANS. y = (1 + cos x)(c + x – sin x).

A: see below the calculation and answer

Q: 2 sin(x) cos(x) + v2 cos(x) = 0 COS

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Q: 2) Proof that If y = f(x) = = cos x then dx sin x

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Q: Calculating derivatives Find dy&gt;dx for the followingfunctions

A: The given function is y=sinx+cosx

Q: Sin x 10. y = 2+Cos x 3 2+Cos x Ob. (2+Cos x)? Cos x C. (1+Cos x)2 1+2 Cos x d. (2+Cos x)? Oa.…

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Q: 2 Find the x-intercepts of y = 2 sin x + sin x – 1 on the interval [0, 27). %3D

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Q: | -sinx. cos* x. dx = O cos*x X. + C 4 cos x + C 5 O sin x + C 5 O None

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Q: 30. y+y" = 0; 1, x, cos x, sin x, (-x, x)

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Q: sin.x 14. What is y" if y=1-cosx A) y'= B) y'= -COS.X (1 – cosx)? sinx (1-cos.x)² C) y'= D) y'=…

A: Given: y=sinx1-cosx We have to find y''.

Q: Find y' if y = 5x sin x. O A. y' = - 10 cos x+ 5x sin x B. y" = 10 cos x- 5x sin x C. y' = - 5x sin…

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Q: 4) f(x) = V1- x² sin-(2x + 1). %3D y 5) tan(x - v) =

A: As per guidelines we have to solve one question  Please repost other questions again

Q: 19 The range of y = sin x is _______. y ≤ 0 -1 < x < 1 y ≥ 0 -1 ≤ y ≤ 1

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Q: 2 (sin x cos x + x) + C - 2 (sin x cos x + x) + C (sin x cos x + x) + C -(sin x cos x + x) + C [(cos…

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Q: y + y tan x = cos x; y(x) = (x + C) cos x, y(n) = 0

A: Given that, y'+ytanx=cosx     ---1yx=x+Ccosx      ---2y0=π We need to verify whether equation 2 is a…

Q: 2. The distance between the points (sin x, cos x) and (cos x, -sin x) is: А. 1 В. V2 C. 2 sin x cos…

A: To find the distance between the two points

Q: 2 sin(x) cos(x) V3 cos(x

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Q: Second-order derivatives Find y″ for the following functions.

A: "Since you asked multiple questions, we will solve the first question for you. If you want any…

Q: Find y' 1. (x-y)2 = sin x + sin y

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 6 sin° x+ cos° x dx sin xcos x Evaluate :

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Q: Find y" if y = 5x sin x. O A. y" =5 cos x- 10x sin x O B. y"= - 5x sin x OC. y"= - 10 cos x+ 5x sin…

A: Solution: The objective is to find the double derivative of the given function

Q: Find y " if y = 2x sin x. O A) y" = - 4 cos x + 2x sin x O B) y " = 2 cos x - 4x sin x C) y " = - 2x…

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Q: y. x -. cos(- + cos(- 2 4 х — у, 2 sin(- 4 = cos x - sin y 2

A: Here, the objective is to prove the following: 2sinπ4+x-y2cosπ4+x-y2=cosx-siny

Q: 6. sin x (1 + sin x cos x) dx y csc² ( tan (y²)) dy 7. cos²(y²) sec (11w) tan (11w) V (2 – sec…

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Q: 0sin 2 x coOS x dx

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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: 1. %3D X sin y - y cos x = C

A: We differentiate the equation and get:

Q: Find y" if y = 8x sin x. O A. y" = - 16 cos x+ 8x sin x O B. y" = - 8x sin x OC. y" = 16 cos x- 8x…

A: If y= 8xsinx then find y''

Q: 26. y' +y tan x = cos x; y(x) = (x + C) cos x %3D

A: 26) Given:             y'+ytanx=cosx         y(x)tanx+ddxy(x)=cosx The differential equation has the…

Q: √x(y)²-(√x cos √x - sec √x)y'=1

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Q: (1 + cos x)y’ = sin x(sin x + sin x cos x – y)

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Q: (x²c ?cosh(sin(x - ): x-w)= – y)) = (x² cosh(sin(x v+coshz ôvôz

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Q: 8. y'(sin x+ y) = x - y cos x

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