Show that there is exactly one solution f E L'([0, 1]) of the equation f(x) = 7 + sin(x) %3D

Q: Describe the method used to integrate sin" x cos" x, for m even and n odd.

A: The method to integrate sinm x cosn x when m is even and n is odd. We integrate by substituting the…

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

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Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: Solve for the differential of y when y = sinæx, x=-, and dx=- 3 2 4 4 -iN

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Q: Verify that the function y = x sin(x) + x cos(x) is a solution to the differential equation: y" + y…

A: 1 have verified the differential equation by finding each derivatives

Q: S sin x In(cosx) dx

A: To evaluate the integral: I=∫sin x(ln (cos x)) dx Substitute  cos x=t⇒-sin x dx=dt⇒sin x dx=-dt

Q: Se* sin e*dx

A: We have to find integrating of given Questions

Q: This differential equation is linear. What is the Q(x)? * Cosx dy t (y- cosx )dn = 0

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Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

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Q: dy +(cos x)y = sin²(x) using first order linear differential equation. dx Solve (sin x) %3D

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Q: 5.32. z = sin(x² + y?)

A: To find the differentials of third order.

Q: Use integration to find a general solution of the differential equation                  dy / dx =…

A: The given equation is  dy / dx = tan2 x

Q: 2. (cos x cos y cot x) dx + (- sinx sin y) dy = 0

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Q: Prove that the function y = ecos* satisfies the differential equation: y" + sin(x) y' +y cosx = 0

A: Find y' , y" and put into given differentiatial equation.

Q: The Particular integral of the differential equation (Dª – 36)y = cos 6x is PI = cos 6x 1260 PI = z…

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Q: Suppose that the tangent line to the graph of f(x) = x0") at x = 1 is equal to the tangent line to…

A: topic:- application of derivatives

Q: Show that cos x is the integrating factor of the linear differential equation dy/dx= sec x+y tan x

A: Integrating factors are useful for solving ordinary differential equation  that can be expressed in…

Q: For an exact equation, Show that this differential equation cos(x+ y)dx= (3y² +2y+ cos(x+ y))cdy = 0…

A: We  are given the differential equation : cos (x+y)dx+(3y2+2y+cos(x+y))dy=0 On comparing with :…

Q: Use the integrating factor to solve y' = -3a²y + sin(x)e-*, with y(0) = 1.

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Q: Find the solution to the differential equation that satisfies the given condition. I am having…

A: Given differential equation can be written as Integrating both sides , we get

Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) = c₁cos (0)…

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Q: 1. S(esin x cos x - acos 2x sin 2x)dx

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

Q: Use integration to find a general solution of the differential equation       dy/dx = cos 2x

A: The given differential equation is  dy/dx = cos 2x.

Q: Show that sin(x^2) ≤ sin x for 0 ≤ x ≤ 1. Deduce that sin(x^2) dx ≤√2/2 on the invterval [0, π/4]

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Q: 1) S ur [sin(In x)+cos(ln x)]² dx

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Q: Integral of e^(4x)sin(4x) dx

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Q: )Show that given differential equation is exact hence solve it (cos a sin a - xy²) dx + y(1 – x²)dy…

A: We know that the differential equation  Mdx+Ndy=0 is exact if ∂M∂y=∂N∂x Given differential equation…

Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

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Q: Find the differential equation corresponding to y=a cos (logx) +b sin(log x)

A: Chain rule of differentiation: [f(g(x))]'=f'(g(x))g'(x) Formulae used: ddxcos x=-sin xddxsin x=cos…

Q: Answer the following using Variable Separable in Differential Equation. sinxsin ydx + cos x cos ydy…

A: Given: sinxsiny dx+cosx cosy dy =0 Solve this by Variable separable in Differential Equation.

Q: Show that the sine integral satisfiesthe (differential) equation xS'(x) + 2S''(x) + xS'''(x) = 0.

A: Given information: Sx=∫0xsinttdt To prove xS'x+2S"x+xS'''x=0

Q: Find complementary function and particular integral of d²y - y = xe* + cos² x dx2

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Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

A: First Solve differential equations ,

Q: Solve the integral. cos x dx J (1+ sin² x) arctan (sin x) 10.

A: To evaluate:                      ∫cos x(1+sin2 x)arctan(sin x)dx    ... (1)

Q: (3tan x – 2cos y ) sec 2 xdx + tan x sin ydy = 0 %3D

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Q: 2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log…

A: First find the domain of f1x=cos-12x1+x2: The domain of cos-1x is -1,1. Therefore, -1≤2x1+x2≤1 Now,…

Q: dy 3-cos?x sin x dx + cos³ (x)y = 1

A: We have to find the solution for differential equation.     According to our guidelines we can solve…

Q: Use the method of undetermined coefficients to solve the differential equa- tion: y" – 2y' + 2y =…

A: Here by using the method of undetermined coefficients we have to solve the given differential…

Q: (0)3-3x+2 sinh' (In x) cosh (In x) (E) sin(2x)dx dx N

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Q: The Bernoulli's equation dy +ytanx = y'sec x after multiplying dx -2y and use appropriate…

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Q: Find the definite integral of sin x -dx 0 1+cos x

A: Given: I=∫0π2sin x1+cos xdx

Q: Solve the differential equation dy tan y x Cos x 3 dx

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Q: 2 sin x f(x) = 1+2cosx 5. Pvaluated at x = 1 rad

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Q: Demonstrate that the function f(x)= e^-x sin (x) is a solution for the differential equation f(x) +…

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Q: Solve the differential equation. dr sin 0 +(cos 0)r = tan 0,0<0<- %3D OP (Use parentheses to clearly…

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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: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) = C₁cos (0)…

A: Sol:- While solving the question , initial θ is considered as 't' At the end , we will replace t…

Q: Live of y = e(x+ln x) cive of ƒ(x) = 5x6 – sec jye of y = e(sin x) e(sin x) - sin(e

A: We have to find the derivative of the given function