n= (-1)" n2 +1' M8 n=1 1 12 +1

Q: Ex: Given the periodic lenchon o< ×<ス 2くメく3 Frd the Fourier ser.es of finy

A:

Q: find the root of the equation  f(x)= -x/2 + sinx =0 using bisection method in the interval [1,3]…

A: given function fx=-x2+sinx=0 find the root of the equation using bisection method in the interval…

Q: The trigonometric substitution x - 2 = 3 sec could be useful in integrating a function (i.e., an…

A:

Q: 1/a | sin(t")dt Find lim T.

A: We have to calculate the value of : limx→∞∫01xsint2dt·x

Q: • Sl-+2u* + uP)du No appropriate Match Question 6 o S(-uP-2u7 - P)au Match the integral expression…

A:

Q: Encontrar la transformada de la función periódica, cuyo periodo es 2 si 0 < t < T f(t) %3D T - sim <…

A:

Q: Assume that f and g are harmonic functions in R^n. Show that div(f ∇g − g∇f ) = 0.

A: Ans- We can start by computing the divergence of the vector field F = f∇g - g∇f:

Q: e cosl – i e™ sin 1 + e¯ cos 1 - i e- sin 1 2 e cosl + i e™ sin 1 – e- cos 1 + i e¯I sin 1 -TT 2 e…

A: Simplify the given expression: Coshπ-i

Q: Prove the Calculus identity sin-(x) + sin-(/1 – x²) 2 x € [0,1], where sin-, denotes the usual real…

A:

Q: ) Prove that tanh'x = tn/itx, X€ (-1,1) i) , Sinh 'x and tanh'x Find the derivative of coch'x

A: (1). We have to prove that:   tanh-1x=12ln1+x1-x

Q: se-2s -)=D 's²+45+3

A: Given,

Q: Q.1 In the study offrost penetration in highway engineering the temperature T at time t hours and…

A:

Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

A: Since you have asked multiple questions in the same request, as per the policy, only the first…

Q: Integrate f(z) = (7)° counterclockwise around the unit circle, using Cauchy's integral theorem if…

A: using cauchy residue theorem to find given integral...

Q: Y 4 1.2) ["se sec ¹ √e de e 20) ff 2² 1 x² ln x dx

A:

Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

A:

Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (3e' cos t)…

A:

Q: What is the amplitude of a sinusoidal function having a maximum of 7 and a minimum of 1? (A) (B) 3…

A: The sinusoidal functions are usually represented in the form of f(x)=asinbx+c+d. For a sinusoidal…

Q: d Find the derivative e" + sin ax] dx e" – a cos (ax) e" + a sin (ax) e" + a cos (ax) e" + sin (ax)

A:

Q: 9. Find the indefinite integral. 1 36+ (x – 4)2 X -4 arctan 36 +C a. 36 オ-4 b. 36 arctan 36 1 x-4 +C…

A: (9) Given: The integral is  ∫136+(x-4)2dx

Q: Q3) Simplify (if necessary) then Compute: y"+ 2y Where y(x) = (z²x + cosx*)] [4(cash2x-sinh2x)] (16)…

A: Given that, y(x)=∂2∂x∂zz2x+cosx44cosh2x-sinh2x16cos2πxddx(2x2) This can be rewritten as,…

Q: a) Use suitable sum and difference identities for hyperbolic functions to show that sinh(5x)…

A:

Q: Recall that sinh(2) = }(e² – e¯²). | (i) Show that all the roots of sinh(z) are of the form zn =…

A:

Q: (1 point) Approximate cos(4.6) using a quadratic approximat First note that cos(4.6) cos(3/2). Let…

A:

Q: (1 point) Check by differentiation that y = 3 cos 2t + 3 sin 2t is a solution to y" + 4y = 0 by…

A:

Q: 1 Q #8 Using implicit differentiation, prove (arctan x)' = - Similar to proofs of (arcsin x)' and…

A: The given data is: Using implicit differentiation, prove arctanx'=11+x2