If z + In(e 2 – e" + e*) = 0 -2x az find at the point (0, 0) O-3 O 3 O-2 O 2

Q: • Let X1,...,Xn iid Poisson (0) such that E(X1) = 0. Suppose that Find the level a = 0.05 LRT for…

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Q: Show complete solution. Expand, that is, perform the indicated operations on the differential…

A: We have to find out the operation

Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian. b. Establish…

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Q: Evaluate the integral. S 20x cos x dx Select one: O A.80 sin. 1 40x cos + C O B.20 sin n1)x+ 40x cos…

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Q: 22. Solve 0 0, x > 0, Urr + Uyy = 0, u (x, 0) = f (x), u (x, 1) = 0, u (0, y) = 0, и (х, у). O…

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Q: Prove 8xyz < (x + y)(y + z)(x + z) for every x, y, z E [0, +∞[.

A: We have to prove given identity: Concept:

Q: 2 3 let (4-x2) 2 dx , write the integral by using Beta function 0. 1 5 8 B 22 .a 1 3 8 B 2 2 B 3 5 2…

A: Substitute x22=t in the integral:  ∫024-x23/2dx=8∫021-x223/2dx…

Q: integral from 1 to 2 of (e1/x^3 ) / x4

A: To evaluate

Q: 5 Evaluate the integral 2x cos(xy)dydx 4 0.

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Q: What does Cauchy's Theorem 6.2 guarantee for the IVP dy dt y cos (t), y(to) = Yo a solution exists…

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Q: solve: 3 (b) uloy) = ity ² "x = 0 w(x, 3x) = sin x = 0 Wyy u(x,0) = sin x wy (x,01 = cox { (c) in R²…

A: Solution

Q: 1 prove that | e -ym dy = mr(m) -ут

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Q: 4 – dt 2 cos 4t 1.

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Q: 8 2 1. Reverse order, then integrate Sr) dydx.

A: Given:    Intergral is given

Q: Aşağıdakilerden hangisi (arctan(ok*) 1+e2kx 2dx integralinin sonucudur ? A)…

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Q: Let f(x, y, z) = ln(x² + z) + y²e"z – cos(2yz). Find fzya- CoS %3D

A: use partial differentiation for finding the derivative.

Q: 12. Suppose that g is integrable and that g(x)dx = -7 and [8(x)dx = 2. d: g(x)dx

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Q: 7. Which of these is a non-elementary integral? In(2y² + 1) А. -dy 4y e-x cosh(2x) В. c. [ e-x +…

A: Non-elementary integral for a given elementary function is an  indefinite integral that is, itself,…

Q: Evaluate the integral. Sex. cos 3x dx e2x [ sin 3x + cos 3x] + C O e2x [3 sin 3x + 2 cos 3x] + C 13…

A: Given: ∫e2xcos3x dxe

Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D

A: Given w = x2x = sin(r2s)

Q: If ulr. 0) satisfies V'u = 0 inr<1, u(1, 0) = S(e). show that Poisson's integral formula in R' takes…

A: Given, ur,θ=0 satisfies ∇2u=0 in r&lt;1. Also u(1,θ)=fθ To show ur,θ=1-r22π∫-ππfϕ1-2rcos(θ-ϕ)+r2dϕ…

Q: Evaluate the integral. 5n /2 2, 1 - cos t dt 3π/2

A: ∫3π25π21-cos2tdt=∫3π25π2sin2tdt=∫3π25π2sintdt=∫3π22π-sintdt+∫2π5π2sintdt=1+1=2

Q: az az and as Use the chain rule to find at (=) Z = tan V u = 8s + 5t, v = 5s – 8t az as az at

A: Topic:- derivatives

Q: Evaluate the integral. 3x cos 2x dx O e3x [2 sin 2x - 3 cos 2x] + C 13 O 1 [2 e3x sin 2x + 3 cos 2x]…

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Q: 10. Find the integral of dx x²-4 O In() + C x-2 O In() + C 2x x+2 O fIn( *2) + C X+2 O In() + C x+2…

A: *using concept:- 1. Partial fraction. 2. int(dx/x) = ln(x). 3. ln(m) - ln(n) = ln(m/n).

Q: Evaluate the integral. 1 cos 2t dt 2 7x/2

A: To evaluate the given integral.

Q: 2. Z=e Iny

A: Given that, z = ex ln y x = ln (u cos v) y = u sin v We have to fin dz/du and dz/dv. Then we get,…

Q: 1 Verify Eular's theorem for z=- =(x²+xy+y*)' x²+xy+y² 2

A: The expression z=1x2+xy+y2=x2+xy+y2-1. We have to verify the Euler's Theorem.

Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

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Q: If f(z,y, z) = I COs(2y – 2). compute and af and Te Əz =I Cos(2y -2). compute O = cos(2y2) I sin(2y…

A: If fx,y,z =xcos2y-z....icompute dfdx and dfdz

Q: 3.12 Еxpress lim n00 n k3D cos 1+ as an integral. (Be sure to include the lower and upper limits|of…

A: Given: limn→∞ 2n∑k=1ncos1+2kn To convert this into the integral , use the following method

Q: Prove that v = In [(x-2)^2 + (y - N)^2] is harmonic in every region does not include .the point ( 2,…

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Q: Assume that after w months, butterflies’ populace in 1000 is calculated as: f(w)=12w+cos⁡(16w)+n×100…

A: Given: Butterflies’ populace after w months is given by f(w)=12w+cos⁡(16w)+n×100 in 1000 where n=824

Q: | 45. Apply integration to the expansion 00 =E(-1)"x" = 1- x+x – x +.. 1+x n=0 to prove that for -1…

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Q: Integrate the fuackion f=g regian bonndel by y the en6* y-o ver

A: The function is fx=xyThe region is bounded by y=x, y=6-x, y=0

Q: per integral test, (-1)" A) Σ B) none of these en (-1)" dz behaves like

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Q: En=1" Vn sin а. 1 b. 2 c. Converge

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Q: (1) xyy' + y² = 2x O separable exact O linear in x O linear in y O homogeneous Bernoulli in x…

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Q: show that f(z)=(z-1) cos(1/z+2) has an essential singularity at z=-2

A: Introduction: Laurent series has an important role in determining the singularities. Suppose, a…

Q: |1) Use a sine expansion to compute the solution of ( ди д'и at ôx? u(0,t)=u(1,t) = 0,t > 0, u(x,0)…

A: According to the given information, it is required to compute the solution of the given equations.

Q: 2. Test for exactness and find the complete solution of n dx + {In(2x – 2) + dy = 0 - (х-1)

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Q: Compute the general antiderivative S a"-1 cos(x")dx COS where n > 1 is an integer greater than 1.

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Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: 2 1. Evaluate the integral: dx 2 x2-x

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Q: 18. Show that Ein d(k)³ = (Ekin d(k))² for all positive intege m

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Q: In x + In(x – 1) = 10 In(x + 25) – In(x – 1) = 3 e2x – 2ex = 15 e2x – ex – 12 = Q %3D %3D -

A: i) ln x+ln(x-1)=10ii) ln(x+25)-ln(x-1)=3iii) e2x-2ex=15 Note:      Multiple part question are given,…

Q: 5. Show that |Logz|<|In(z)|+ t, for all z # 0.

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Q: Evaluate Poisson Integral: In(1-2a cos(x) + a²) dx ,a.) [a| 1,

A: To evaluate Poisson's integral: ∫0πln1-2αcos(x)+α2dx  a)α&lt;1 b)α&gt;1

Q: If In |(In x)" dx, show that In = x(In x)" – n.Ip-1- Hence find nx)* dx.

A: I am going to prove the given identity by using integration by parts and then use this identity to…

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.