Q3/ Find Fourier cosine transform of the function f (x) = 2x ,0 < x < 4

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: A linear differential operator g D is called    annihilates the functions fx if and only if…

Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

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

Q: Find the critical points of the function f(x)=sin2x−cosx on the interval (0,2π).

A: For critical points, first find the derivative of the function and equate it to zero.

Q: sin(x) + 2 x4 +1 5. Determine if the integral dx converges or diverges.

A: Cauchy integral test : For an&gt;0,let ∑n=λ∞an is a series of positive  terms. Then ∑n=λ∞an is…

Q: t2 sin wt

A: We have the formula  L{tnf(t)}=(-1)ndnFdsn(s), where F(s)= L{f(t)}

Q: Kim throws a ball against a wall at time t = 0. At time t = 1, it hits the wall and then at time t =…

A: The objective here is to check whether Mean Value Theorem can be applied to show that at some point…

Q: Write down Fourier Transform for the following non periodic function.

A: In this question, we have to write the Fourier transform of the non-periodic function. The function…

Q: [11 sec²(x) dx convergent divergent

A: We have to check that given integral is convergent or not.

Q: 4. Determine exact values of 0 if 0 < 0s 2n given that tano - V3. Explain your process.

A:

Q: What is Properties of fourier transform

A: Properties are:-  1.Linearity 2. Time shifting  3. Congugation 4. Area under x(t) 5.Area under x(jw)…

Q: Find the exact error in approximating ln(sec(−0.4))by its fourth degree Taylor polynomial at ?=0.

A:

Q: Find the indefinite integral and check the result by differentiation. dx 9x2 Part 1 of 7 Observe…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Let D be the differential operator ddx, we have t find function f such that  fDgx=0, where…

Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: Find Fourier transform for f(t) using differentiation property x(t) -2 3.

A:

Q: Find total differential of function u = x.

A: 6. The given function is u=xyz. We know that the total differential of a function u=fx,y,z is given…

Q: 2.) у" - Зу' — 2у %3D0 У (0) %3D0, у'(0) %3D 9 ,у" %3D0

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Q: f(x) = cos(T.x)+ sin(27x).

A:

Q: respect to x of/ /(3Vi-1) dt is 3x – 1 by the 2nd fundamental theorem of C The derivative with (A)…

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Q: Use Fourier cosine transform to solve y" – y = 3e-4 y' (0) = 0 lim y (x) = 0, as x → o0

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Q: Integrate the function. Vx2+36 dx 5x2 Select one: A In x2+36 А. 1 + x/ - Vx2 + 36 + C 5х В. Bx + In…

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Q: Find the indefinite integral and check the result by differentiation. dt F--3-3)- 8. 12

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Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

A:

Q: 000 Find the solution of heat equation by Fourier sine/cosine transform, if initial temperature is…

A: Here we use separation of variables. Means we assume that  ......(i)  be a solution of the given…

Q: ) 3x - 4x= sin社 ; at t=0,x==

A:

Q: Find the Laplace transform of tant. Show your full Solution.

A:

Q: Find the linearization of ƒ(x) = √(1 + x) + sin x - 0.5 at x = 0.

A: substitute 0 for x in f(x)=1+x+sin x-0.5 to obtain the value of f(x) at x=0 f(x)=1+x+sin…

Q: Find the equation of the normal line to the curve f (x) = 6e2x cos x at the point (0,6). %3D

A: Now point on the function is (0,6 ) . Step 1 : find the value of the derivative at x=0 . So, f(x) =…

Q: Find Fourier transfarm f x #1= cos aut ut

A: Given the x(t)

Q: Calculate the derivative d dz (2t5 34 dt using Part 2 of the Fundamental Theorem of Calculus.

A: The solution are next step

Q: By integration find the Fourier transform of Ax)=2r+1 _if þx|<1_and fx)=0 otherwise.

A: According to our company policy, I am supposed to answer only one question at a time. For the rest…

Q: у %3DIn(In sec x)

A:

Q: find the fourier series for the half-Periof sine of the function fxj = sinx inthe period x Then find…

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Q: Prove that the Fourier transforım of f' (x), the derivative of f (x) is – ip f (p), where S(p) is…

A: Answer: For the given data,

Q: Find the differential of the function.

A: Differentials are infinitely small quantities. We usually write differentials dx, dy, dt (and so…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: See the detailed solution below.

Q: fer) sen ax %3D

A:

Q: 1: Find the derivatives of: 1+ tanh x a) y = In ソ= %3D 1- tanh x b) 2 y= cosh? 1-x? 1-x

A:

Q: ind the 9th derivative of f(z)=exp((-1 + isqrt 3)z) at z=0.

A: Given f(z)=e(-1+3)z Differentiating w.r.t 'z' f'(z)=e(-1+3)z(-1+i3) f''(z)=e(-1+3)z(-1+i3)2…

Q: Prove the following continuous time Fourier transform relationship. sin(at) 1 X(N) = Continuous Time…

A: Fourier inverse of XΩ=1    -π≤Ω≤π0    otherwise is : F-1XΩ=12π∫-∞∞XΩejΩtdΩ…

Q: Show complete and orderly solutions. Simplify all final answers whenever possible. Using…

A: L(Cosh at).

Q: Find the sine transform of and deduce that TUX e 1 tanh (p/2). |(2x) F, (cosech rx) = %3D

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Q: Verify the differentiation formula.

A:

Q: What is the substitute of the expression (9+x)/2 if [ dx -is transform by trigo substitution…

A: In the question we have to find substitution for given integral value.

Q: Calculate the derivative 33 4:6 dx using Part 2 of the Fundamental Theorem of Calculus. 33 dt = da

A:

Q: limit x approaches zero, sin^2x/x

A: Given,

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The given function = 10x+ 9x2-sin6x