2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

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Q: The linear approximation at x 0 to sin(2x) is A + Bx

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Q: 7. Find the dy/dx of * y = In sin 5x

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Q: 1- Find the equation of the tangent to the curve y = 2 sin x+ cos2x at the point x = n. 2- Find the…

A: Solution:

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Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: x sin wx dx x2 + 6x + 10 Show that (2 sin 3w – 3 cos 3w) w > 0 %3D - 2e2w

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Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0 |

A: We will find out the required solution.

Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B} sin²x + C {C}-{cos²x + C {D} sin 2x + C

A: A detailed solution is given below

Q: I Eliminate the arbitrary constants -2x 2X Y = C,e cos 2× + Ge sin 3X

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Q: Find the general solution of y′−y=sin x + cos 2x using variety of parameters

A: Given that: y'-y=sinx+cos2x To compare the given differential equation with standard form of…

Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

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Q: y f(x)sin2x + g(x)cos %3D x) =tan3x x)% sin3x %3D - r) =cos3r

A: Differential equation: y''+9y=tan (3x)The auxiliary equation is,m2+9=0m=±3iComplementary function…

Q: y = (sin x +cos x) sec x = sec² x

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Q: 3. Explain graphically: cos x dx = 0.

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Q: Solve if the set of functions (1, x, sin x, e^x, cos x) is linearly independent or dependent…

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Q: The integrating factor of the LDE y'=x-2ycotx is A B с D sin²x sec²x csc²x cos²x

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Q: Show that : y' = 1 when y(x) = sin-(x) %3D V1– x2

A: Differentiation is done in many ways. Some of the rules of differentiation are illustrated below :…

Q: To evaluate 3cosx -1 1- sin?x dx, the integrand can be transformed to A J(3 cos x - sec²x) dx ® S(3…

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Q: At what points the curve x = 2a(cos(t))-a(cos(2t)), y = 2 a(sin(t))-a(sin(2t)) has vertical and…

A: Given: The curve equations are shown below. x=2acost-acos2ty=2asint-asin2t Calculation:…

Q: dz 1) Find ifz = 3 cos x – sin(xy),x =y = 3t - dt

A: NOTE*** As per bartleby guideline for more than one question asked only first is to be answered…

Q: 2. Evaluate: S(cos x)(In sin x)dx A. sin x (1 – In sin x) + C C. sin x(In sin x – 1)

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Q: 11.) F sin (x)cos²(x)dx 2

A: Note:   As per our company policy we should answer only one question each time, so please repost the…

Q: 2. Find the length of the curve: y = 2 In (sin (÷x)); -< x

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Q: Show that sin x dx=1-cos t (0<x<t<}r).

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Q: Find the complete solution of ey sin x dy cos²x = 0 dx

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Q: Find the linear approximation to h(y) = Sin(y+ 1) at y =0 Use the linear approximation to…

A: This is a problem of linear approximation.

Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: tan st e dt 2

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

Q: What is if z = x'y+ sin(xy²)?

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Q: 2. Show that the LT of sin(wt) is L sin(wt)] (s) where w is a positive constant.

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Q: Find y' , for y=Sin-1(Cos√x)+Cos-1(Sin√x)

A: The solution for the above question is as shown below.

Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: 2 Given that: J2(x)=-, cos.x + sinx find J(x)

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Q: Find the general antiderivative of the given function. sin( x/7π)   and  sec2(5x) + sec2 (x/3)

A: GIVEN DATA : Function sinx7π and sec25x+sec2x3        TO FIND : Anti derivative of the function…

Q: Find the solution of the equation z az cos y which tends to zero as x o and has the value cos y when…

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Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

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Q: Find the solution of the equation = e Cos y ax ay which tends to zero as x → 0o and has the value…

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Q: The linear approximation at x = 0 to sin(6x) is A + Bx where A is: Preview and where B is: Preview

A: First of all, consider the formula to find the linear approximation at any point a for function any…

Q: b f sin'x. cos²x.dx ef cos(Inx).dx C-

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Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

Q: Q1) Show that: (a) (1+x)° =1+6x :(cosx) = dx = -sinx (e)읊 = E d ( V) = (d) V1+ tan x = 1+;x dx 2 vx

A: NOTE: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 3. Find d, where ; a) cos(xy)- (x+y) (x+ =2 + e

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: (a) f* (1 – cos 3t) sin 3t dt,

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Q2: (a) Evaluate ſ cosx sinx V1 – sin4x dx.

A: