Known: I(v) = 2n2²E, p(e) « e To, e = nhv, n: any positive integer = E P(e) € n=1 > p(e) = 1 n=1 Prove that: hv hv ekgT – 1 - (for 0

Q: 5. A clamped cubic spline S on [0, 2] is defined by So(x) – 1+ Ar + Bx - 23, 0<x < 1, S(x) – S1(x) –…

A: Using the conditions of cubic spline,

Q: 1. Aşağıda verilen serilerin yakınsaklık ya da ıraksaklığını belirleyiniz (Yöntemleri açıklayınız).…

A:

Q: 3 > sin/ Vn2 2 n=1

A: To check the convergence of the series

Q: By writing the ODEs in their normal form near the bifurcation point show that (a) ˙x = 1 + rx x…

A:

Q: 10. Let /=x'dx. (a) Use the FTC to evaluate I exactly. (b) Compute the actual approximation errors…

A: Note : There are many subparts in the question and other subparts are incomplete due to…

Q: 3. Let X1,., Xn be iid Uniform(0, 3) where 3 is an unknown parameter. You can following fact without…

A: given that

Q: =0 in (0,0) and T(x,t)= 0 at x= 0, l for all te[0,0).

A: Given that the heat conduction G in a bounded domain [0,l] ∂T∂t-∂2T∂x2=0with T(0,t)=T(l,t)=0the…

Q: 8. The integral What is the value of A. B. can be rewritten as 15x²x³43x - 19 (x + 1)²(x² - 6x +13)…

A: Let's find.

Q: Which of the following is a left Riemann sum approximation of (x²) dx with n subintervals of equal…

A: Definition used-                  Left-hand Riemann sum -                   ∫abf(x)dx=…

Q: 2 Find the n th Lerm of the following Seq Uin Ln 2 2. Ln3 3. n= ,2,3,Y; -3 n=1,2,3,4 (2 Test the Con…

A:

Q: Let t> 0, 1 > x> 0 x = 0 or x = T, t>0, t = 0. 1, 4:(x,t) {0, %3D sin x, 0 sxST, (a) Show that u, is…

A: Given Boundary Value Problem ( A )  : ( ∂2∂x2-∂∂t )u =0  , 0&lt; x&lt; π , t&gt; 0…

Q: Let X1, X2,, X, be iid N(0, o?). Consider the hypothesis test: Ho : o = 1 H : o² = 4 Let C1 = {(s')²…

A: Let X1,X2,..,Xn be iid N0,σ2. Consider the hypothesis test: H0:σ2=1H1:σ2=4 Let C1=s'2≥K1,C2=s2≥K2…

Q: -пя for all x € 0, 00). t fal(x) — же па for all z € [0, co). Find || fn||sup for all n. Prove that…

A:

Q: FIAD THE OTER FIXF FUH aiON OF ĦF xauTF XHGUE X O SIn X =3

A: The given function is:sinX=35To find other five function

Q: 40E (mod 3) W = 1 入 人 7 11 2 4 To solve this problem should use the function on the oyou value. scme…

A:

Q: 3) Suppose that g is a Riemann integrable function on [0.3,31.5] and f(x) = g(x) except for the…

A: This is a question of the Theory of Reimann Integration.

Q: The modified Bessel function I,(x) has the integral representation 2 7/2 El cosh(x sin 0 )do. n Jo…

A: Given:

Q: I don't understant this hw problem

A:

Q: 1. Aşağıda verilen serilerin yakınsaklık ya da ıraksaklığını belirleyiniz (Yöntemleri açıklayınız).…

A: As you have asked for only question number c, so I am only giving solution of that.

Q: xy" -yl=o has an infinite of soluhons. However reimber soluhion sahisfies these y co) =O, y'cool…

A: Let us solve the given differential equation xy''-y'=0 For the second order Euler homogeneous ODE of…

Q: 2n The space is C[0,2r] and the inner product is (f.g) = f(t)g(t) dt. Show that sin mt and cos nt…

A: We will show the following given result.

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: 4. ·| cotl t• dt 0. lim limitinin değeri kaçtır? n In(x + 1) a) 3 b) 1 c) O 2 d) 4 Boş bırak

A:

Q: use the form of the definition of the integral given in theorem 4 to evaluate the integral

A: Given an integral

Q: #3. Suppose that h(x) is integrable and that ,h(x)dx=1 and S,h(t)dt = 6. Find a. Sh(x)dx b. –…

A:

Q: 6. Consider the ODE system below f = y? - ,2 = y +?. Which of the following is true? a. Solvable by…

A: Here we have given two differential equations. For a system of ODEs, we can use the elimination…

Q: Let C be the shortest path that connects a to ni and I = . (sinhz + 1)dz %3D O I-sinh rt+ T(i-1) O…

A:

Q: 1-cos(z) if 0 < z < ™ X has PDF f(1) = %3D .0 otherwise Find the probability P(0.64 < X < 2.76).

A:

Q: (e) The solution, u(x, t), of a wave eqution on a closed interval under certain conditions is given…

A:

Q: A circular ring of wire of radius ro lies in a plane perpendicular to the x-axis and is centered at…

A:

Q: The bounded solution of Laplace's equation Upr +Ur + uge = O outside the circle r 3 which satisfies…

A:

Q: The modified Bessel function I,(x) has the integral representation 2 (7/2 1,(x) = n Jo cosh(x sin 0…

A: We will use simpson 13rd  rule  ∫abf(x)=△x3f(x0+4f(x1)+2f(x2)+.......+2f(xn-2)+4f(xn-1)+f(xn)

Q: If /has an isolated singularity at z a and /(2)- an(z-a)" is its Laurent's expansion about z a. Then…

A: We are provided that f has isolated singularity at z=a. The Laurent's expansion about…

Q: Let X1, X2,..., X, be i.i.d N(0, 1). e most powerful test for testing H : 0 = 0 against K > 0. ower…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: A ) find me heneral solutron and the Particular solutim S at isfying for the inidraI condition X"…

A: Answer

Q: Consider the 1-D Burgers' equation in [-1,1] ди a?u дии + at The initial condition is: u(x, t = 0) =…

A: Solution is below

Q: I need help with number 19 using the substitution formula. Can you please explain how it works…

A: We need to apply the method of substitution to compute the given integral

Q: Let X1, · , X, be iid N(µ, 1) where µ is an unknown parameter. Consider the hypothesis test: Ho :…

A: 3. From the given information,

Q: Two resistors in an electrical circuit with resistors R,and R, connected in 1 -=- +- 1 1 parallel…

A:

Q: Q5) Use Simpson's 3/8 rule to compute the approximated solution 1 wiere f( = defined at the interval…

A:

Q: Compute the Riemann sum for the double integral R (8x – 3y) dA, where R = [1,7] × [1,5], for the…

A: Given

Q: 7. a) Show that F(x,y)= is a conservative field. b) Find a potential function ø(x, y) fa [show your…

A:

Q: Find the antiderivative of |5sin x In5 cos x dx · O 5cos x + C O 5sin x + C O 5sin x In 5 + C O 5sin…

A: To find the antiderivative of:∫ 5sinxln5cosxdx

Q: Create a unique aNadratic furncbion in vertex form Ehat mects the following criteria: - hos an aris…

A: Given: For quadratic equation  the axis of symmetry x=-5 minimum of y=-9 wider than the quadratic…

Q: Let f:R^2 --> R^3 be given by f(x1,x2)=(e^(x1+x2^2, x2+cos(x1,x2), x1^2+x2^2+2) Compute the…

A: Using jacobian matrix,

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

A:

Q: Let C be the shortest path that connects a to ni and I = fe (sinhz + 1)dz. Then None of these O…

A: Evaluate this integral from initial to final point.

Q: (e) dy = separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y none of…

A: Let's solve for diffrential equation.

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.