Find Taylor's Sen'ed fey ci) f(x) = sin (2) about x= 1

Q: 8. Evaluate the integral. sin x xp. 4+ cos x

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Q: Find the indefinite integral. ∫cos3 x sin4 x dx

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Q: Evaluate the definite integral. π/2 1- cos(2x) dx

A: Answer:-(1) Given the integral,     ∫sin2x cos22x dx=∫44*sin2x cos22x dx…

Q: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

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Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: Evaluate the integral f sin²(3x) cos (3x) dx.

A: The given integral is ∫sin23xcos53xdx. We have to evaluate the given integral.

Q: s nip

A: Given z=tanα2

Q: 29.Verify that W[xλ cos(μ ln x), xλ sin(μ ln x)] = μx2λ − 1.

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Q: 1- Prove that cosh 2x - sinh 2x = e2

A: sol)Given cos h 2x-sin h 2x=e2x

Q: What values of x in the interval [0,2pi] satisfy 2 + 2cos(x) - sin2 (x) = 0

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ (x) has a root in [o,]. If we…

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Q: 2. F(x) = [ cosr' dt

A: Use fundamental theorem of calculus

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: 3. Prove that the identity is true. sin*t- cost = tan²t-1 cos't

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Q: can you prove it, please ? cosh 2x=sinh^2x+1 = 2 cosh^2-1

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Q: Steb by step

A: We will need integration by parts for this problem. So we assume u and dv and from there find du and…

Q: 1. If z = sin2+In^, find the value of x- +y X

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Q: d Prove that sin x cos x from first %3D dx principles only. Be sure to prove any limits that are…

A: Let's learn first principle of derivative because we have to find derivative of sinx using first…

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: Use linear approximations to estimate the following. 1. sin 9/4

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Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: Prove that sinh−1(x) = In( x+Vx2 +1)

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Q: The derivative of the function y = 9 sin + 22 is. 0 + (In 2") O - (In 2)2= O + (In 2)2" 0로+ (In 2)2"…

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Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. .......Integrate f over the given interval of x, using…

A: Solution:

Q: What is the definite integral of sin^5 (x) cos^3 (x) dx if the lower limit is zero & the upper limit…

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Q: Find a real root for x tan x+1 = 0 using Newton Raphson method.

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Q: Evaluate the integral S cos ³ x + 8 sin x cos³² x + 6s in ² x dx; cosx #0 2 cos²x

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Q: 4) u = x² sin=1 x 5) Ø = tan¬1 3 0 6) y = In(7 – 3x)

A: This question is taken from the derivative in which we have to find the derivatives of the given…

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: Find the definite integral of ƒ™/* cos 3x sin 5x dx. -π/4 Option 1: Option 2: Option 3: Option 4:…

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Q: integral of (e^2x)(sin3x) using u=e^2x

A: Given, ∫e2xsin3xdx    We have to find the integral

Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

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Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: Prove that : 1. Sinh'x= In(x+x² +1)

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Evaluate the integral: 3 X sin ³ COS 3 3 X col 3

A: Solved below.

Q: IT Evaluate the integral: (cos x + sin x cosx)dx

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Q: Prove the identity. cosh(x) + sinh(x) - e

A: To prove the given identity we uses basic expression for sinh(x) and cosh(x).

Q: Prove the identity (cosh x + sinh x) n  = cosh n  x + sinh nx

A: Consider the given L.H.S of the given identity coshx+sinhhxn

Q: e). Prove that Sin3A+sinA 25in2A -COSA

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Q: What is the relation between the expansion of cos x, sin x and ex

A: We need to find the relation between the expansion of   cos x, sin x and  eix

Q: cos(9x) -dx COS J 1+ sin²(9x)

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Q: /2 Evaluate using Wallis' Formula: sin5 x cos6 x dx

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Q: 1 Use the definition of the hyperbolic functions to prove the identity 1- - tanh? (2x) cosh (2x)

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Q: The approximation of 1 = f*cos(x³ - dx using composite Simpson's rule with n= 3 is:

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Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: Prove that : 1. Sinhx= In(x+x² +1)

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Q: Prove that for all x € [1, 00), – sinh (- |cosh'(x)|) = V -1. %3D Ouest!

A: Proving of function  sinh(cos-1(x))

Q: 7. Prove that: ++) + sin; + e) = v3cose (3) (a) COS

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