LINEAR DIFFERENTIAL OPERATOR N FUNS TIO

Q: sin z In(sec z) dr

A: Answer and explanation is given below.. For 17 and 18 please repost the questions

Q: artial Differentiation. If u = In(x² + y²) and z = sin ollowing: eva a²u ay?

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Q: Integral family Use the substitution u = x" to show that dr 1 - sechx + C, for r > 0 and 0 <x< 1.…

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Q: De Moivre's Theorem

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Q: Fourier cosine transform of e^-2x + 4e^-3x

A: Solution: Definition The function Fcs is defined by Fcs=∫0∞fx·cossxdx is called Fourier cosine…

Q: Integration Evaluate the following integrals.

A: To evaluate the given definite integral.

Q: Integrating Polynomial Functions integral  sin x/  cos^2   x     dx

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Q: Stokes's theorem is a special case of the theorem of Green.

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Q: Partial Differentiation. If u = In(x² + y²) and z = sin-1 *(÷), evaluat-

A: Differentiate the following

Q: General construction of Riemann integral of function f in ℝ³

A: It is given that Riemann Integral

Q: 1 e function f (x) = ,x E [-27, 2nt| is continuous on: 1-cos x

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Q: 2 2t dt

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Q: OUESTION 2 Show That yi= dx ta ĝ yo =-x° are both soluhions of y= xy'+ (y)? Are the c wn stant…

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Q: sinh (x) esin h-' (x) sin h- (x) Vx²+1 -esin h¯' (x) sin h Vx²–1

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Q: veriby the indicated punction that is Eqyuation.4n Some msaone cases assume Solution of the given…

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Q: integral cos (;- 1) dt. 14. Evaluate the indefinite (u-substitution)

A: We have to find the value of the infinite integral

Q: 5. Find all the first and second order derivatives of the function f(x, y) = x³ ln(y) + ³xy + x²y³ +…

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Q: Fourier series f(x)= x sinx 2 xe (7)

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

Q: LAPLACE TRANSFORM OF INTEGRALS

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Q: 1. Integral family Use the substitution u = x' to show that dx - sechx + C, for r> 0 and V1 - x 0…

A: To show: That ∫dxx1-x2r=1rsech-1xr+C. Formula used: ∫duu1-u2=sech-1u+C

Q: bn =1/n f(x) cos nx dx bn" f(x) cos nx dx bn fo) sin nx dx bn -1/m f(x) sin nx dx

A: Last option is correct.

Q: Evaluate Definite Integral Using Fundamental Theorem Evaluate the integrals using fundamental…

A: To evaluate ∫032sint-2tdt

Q: integrable form of sin-cos-sine 2 2 | u²-1 du sinu du V 1-u2 du

A: We have to choose the correct option according to the given information

Q: f(x) = {cos x 0<x< n n < x < 2n find its Fourier

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Q: Fresnel integral Show that the Fresnel integral S(x) = So sin t² dt satisfies the (differential)…

A: Given Fresnel integral: Sx=∫0xsin t2 dt Use the fundamental theorem of calculus. ddx∫ax ft dt= fx…

Q: lim cos x + x cos a. 0 b. 1 d. does not exist

A: This question is based on Squeeze theorem.

Q: Finite integral: J-2-9 .2.

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Q: Partial Differentiation. If u = In(x² + y?) and z = sin-(=), evaluate the following: azu 1. ax azu…

A: Here is the solution of the given problem.

Q: Arcsin y dy

A: Let us find the value of ∫01Arcsiny dy. This can also be written as ∫01sin-1y dy Let I=∫01sin-1y dy…

Q: NTEGRAL CALCULUS - INTEGRATION BY PART

A: Consider the provided integral, ∫ 4x·cos2-3xdx Solve the provided integral by using by parts…

Q: Find the limit

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Q: Sy cos y· sin²y dy

A: Given: I=∫y.cosy.sin2ydy

Q: A)) Q1/ Find Fourier Sine Integral presentation of the function: f(x) = xe-* , x>0

A: The given function is: f(x)=xe-x ,      x&gt;0

Q: integral: 2² sin (-) dt du Evaluate the integral:

A: use substitution method and integration of parts for solving the integral

Q: Сompute 1. f dx, where f(x)=|x|.

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Q: Inverse identity Show that cosh (cosh x) = |x| by using the formula cosht = In(t + Vr - 1) and…

A: Given : cosh-1(coshx)=x for all x   and  cosh-1t=ln (t+t2-1)    Claim :…

Q: Fourier series fixis = x sinx ,xe (…,7)

A: The given problem is to find the Fourier series expansion of the given periodic function with given…

Q: lim 0 2 + sin(okr }) k=1 6 O A. J(x + sin(2xx)) dx 6 O B. J(2x + sin(2xx)) dx 3 O C. J(x +…

A: Definite integration limit as sum

Q: Formula of Laplace of derivatives of the nth order .

A: Here we need to write the formula of Laplace of derivatives of the nth order .

Q: sech x+csch x Q3: prove that e2x %3D csch x-sech x

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Q: 8. exy = e4x – e5y %3D

A: we have to derivative

Q: Bessel fundion Satis fies veyi fy that the Sinx the Bessel equation of

A: We have to verify that the Bessel function J12x=2πxsinx satisfies the Bessel equation of 12.

Q: partial derivatives of Z. Complete and detailed so Z : Arctan (x²/y³)

A: Given: Z=Arctan x2y3

Q: Partial Differentiation a2z 1. If z = e* sin y + e³ cos x, verify a²z = 0 ду?

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Q: he general antiderivative of a function is also called the. A integrand B arbitrary constant…

A: The general antiderivative of the function

Q: Beta Function 27 dx (*+ 1) Prove that

A: The given problem is to evaluate the given beta function integral.

Q: lim sin(2z) = z-/3 %3D /3 2. 1/2

A: We need to find limx→π3sin2x

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.