Consider the ODE system x' = A et + 3 with A = 4 1 3 a) Use the method of diagonalization to find eA".

Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = tan x, a = π

A: The linearization of a function f(x) at x = a is, Now differentiating  given function with respect…

Q: SEr up AN INTEGNAL KEPRESENTAT7 ON OF THE ARGA OFTHE REFGrON BOUNDEO BY y =x3,y=0, x=-l, X= 2 ド

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: 5) Evaluate the integral.cusc c for the constan6 of integrafion) 2(ean cx) +6an cx>) dx

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Q: Define stpes to obtain the general solution of a 2nd order homogeneous ODE with real coincident…

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Q: SVA- 4-y² √8-x²-y2² z² dzdxdy. √x²+y²

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A: The main reason behind the covariant derivative satisfying Leibniz's rule is it maintains chain rule…

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Q: Find antideriuative Flx) of the an flx) = _8 sinx 13 + COSX functian such that FlO) = 1 %3D %3D

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Q: Evaluate the improper intergal 1 dx using the residue (x2 + 9)* theorem.

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Q: 5. What is UF, where F = 0? Prove the correctness of your %3D answer / computation.

A: To find- What is ∪F, where F = ∅? Prove the correctness of your answer/computation.

Q: Prove that d (sec"x)= 1.

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A: We have to solve given problem:

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A: First evaluate indefinate integral

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Q: y = sech*x = In(_+ V1- x², sechx = In(- 1+ V1-x² Prove that .... ..

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Q: Show that the following line integral is path independent (3,2) cosh (0,0) (8xdx+6ydy) 4.

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Q: Consider the following ODE with boundary conditions y" + λy = 0, y(0) = 0, y' KN ㅠ = = 0.

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Q: Show that the Euler-Cauchy Equation ry" + ary + by = 0, r+0 can be transformed into the constant…

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Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: Step:-1 Note:- 1. ∫∇F.dr =∫fx i +fy j dx i +dy j  2. Fundamental Theorem of Calculus:- ∫bc F'(x) dx…

Q: Evaluate the integral. 2 | 7t sec -'t dt 2113 | 7t sec - 't dt = 2113 (Type an exact answer, using t…

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Q: what local linearizatoin of the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)  (show all steps…

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Q: Let A = LU, where L is lower triangular with 1’son the diagonal and U is upper triangular. How many…

A: Given: Let A = LU, where L is lower triangular with 1’s on the diagonal and U is upper triangular.…

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Q: Show that the line integral is independent of path tan y dr + r sec y dy where C is any path from…

A: Given that ∫C tany dx +x sec2y dyShow that the line integral is independent of path and evaluate the…

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A: We have to apply the Residue theorem to find the value of the following integral : ∫C sin πz2z+12z-2…

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A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: show that the. following Complex functron is dis continuous at z=i. fCZ) = スー! %3D 3.

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Q: Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

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Q: It u-ys Int, Ya っ 3. to ny find by rusing ypropoiate chain rule

A: Given, Let, u=rs2ln(t), r=x2, s=4y+1, t=xy3

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A: Find the integrable form by substitution method

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A: Use the formula of the length of the polar curve. L=∫0πr2+drdθ2dθ Here, r=aθ3 and drdθ=ddθ(aθ3)=3aθ2…

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Q: %3D %3D In MIMI2 9.5. Ly=, Wq= F and L== au Find : Po =? and P,= ?

A: A/B/c Queueing System: A is the interarrival-time distribution. B is the service-time distribution.…

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Q: 2.) given this trigher ODE, use the reduction of HODE via of systems ODE and find the general non…

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Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…

Q: Show that lm Casy -1 CoSy-1

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Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.