Check the following bound under the assumption of independence and dependence tPy < tP, ř:y for t > 0.

Q: Show that limit t  appraoaches infinity  integral -t  to t  x dx =0

A: To prove:

Q: Let F(x, y, z) = 6x?i – cos(xy)(i + 5). Calulate the divergence: div F(x, y, z) =

A:

Q: Show that each function in Exercise satisfies a Laplaceequation.ƒ(x, y) = e^-2ycos 2x

A: Given :

Q: Find the divergence at Iol g0o o) for Hure Vcetor Ficuld F (Xoyaz) =e*sínyi-c" ă cos yjt z°k

A:

Q: Find the set A, whe f is continuous on A. sin(nz) a) S(z) = L n{x* + 2n)' n(x* + 2n)'

A: We shall solve first question only as per the answering guidelines. For others kindly post again by…

Q: Show that if r(t) = ƒ(t)i + g(t)j + h(t)k is differentiable at t = t0, then it is continuous at t0…

A:

Q: Q2) A) Verify that wxy wyx for w x sin y+y sin x +xy. %3D R) Show that f(x v) = e-2y cos 2r…

A: See the details solution in below

Q: Find the Lyplace tiangern f (t) = sin Ct+a) of cor (t-a) usng S e-e f (t) dt f Ct) dt .

A: The given problem is to find the Laplace transform of the given function using integral method.

Q: sume that f(t) is continuous on [a, b| and that u = g(t) is cont ferentiable on [a, b], then f(u)…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 1 et dx 1 (1 — е*)2

A:

Q: Define h(0,0) in such a way that h is continuous at origin       h(u,v)=ln(nu2-u2v2+nv2/u2+v2

A:

Q: T 2 If fo)= J* +?dt, use the fundemental theorem of culculus part 1, to find f'cx) fixs=

A:

Q: Show that the following function satisfies the two-dimensional Laplace's equation. z = In(x² + y²) +…

A: The given function is -  z = ln(x2 + y2) + 2tan-1yx We have to test whether the above function…

Q: If m(E) = 0, show that any function f: E → Ris Lebesgue integrable and Se f = 0.

A: Given, mE=0 So, a measurable function f:E→ℝ is said to be Lebesgue integrable  (or simply inferable)…

Q: Evaluate the integral, if it exists.

A: Given: ∫-π4π4t4 tant2+costdt

Q: Verify the Divergonce Theorem for F=(2x-x)+x*y} -aż? taken over the bounded by x -o, X=1, y=0,…

A:

Q: Consider the slope field shown. (a) For the solution that satisfies y(0) = 0, sketch the solution…

A: Given,  the slope field :

Q: Define h(0,0) in such a way that h is continuous at origin nu? – u?v² + nv² u? + v? h(u, v) = In

A:

Q: Evaluate the integral f(Vt,et) dt. t+1'

A:

Q: Evaluate the integral. T/3 csc(t) cot(t) dt T/4

A:

Q: If foxJ= S** t'dt, use the fundemental theorem of culcolus, part 1, to find f'cx) fixs=

A:

Q: find the divergence of F. F(x,y) = √ +y I i+ Y Pa 꾸

A: F(x, y)=xx2+y2i+yx2+y2j

Q: Assume x and y are functions of t. Evaluate dy/dt for the following.

A: Given equation is 2xey=4-ln1024+10lnx, where x and y are functions of t. To find dydt if dxdt=8,…

Q: Which among the following relationship is known as Divergence theorem? Select one: O E.ds = V x E dv…

A:

Q: Use integration by parts to evaluate lim Sest f(1)dt. (Let u = Z→∞J f(t) and dv = est dt.)

A: As per the question we are given a limit of an integral, and we have to use the integration by parts…

Q: | (t – cos(3t))e-'dt

A: Using definition of Laplace transform.

Q: Evaluate the integral.

A:

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

A:

Q: Compute the integral fo S x cos(xy)dxdy

A:

Q: -> Verify Divergence Theorem for the function F x + y? = 9, z = 0 and z 2. = yi + xj + z? k over the…

A: Given :-  Verify Divergence Theorem for the function  F→ = y i^ + x j^ + z2 k^ over the region…

Q: Evaluate the integral. (Hint: u-sub) R/8 S (1+ etan 20) sec² 2x dx O 2e e

A:

Q: Evaluate the integral f(t) = S tA(t-3) dt t A(t-3)

A:

Q: t * et  Compute the convolution integral.

A:

Q: Evaluate So y? exy dA, where D 'is bounded by you, yit, x

A:

Q: If ƒ is continuous and f(t) dt = 16, find the integral

A:

Q: Use the Laplace transform to solve Utt – Uxr = 100, x > 0, t > 0. u (x, 0) = u4 (x, 0) = u (0, t) =…

A:

Q: Find. the diveraence. and.cur.l.4the fallown Vecter. field: ..F= Xe..y.e. k.

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question....

Q: b) Use the divergence theorem to compute f. F ·ñ dS, where S is bounded by x + y + 2z = 2 located in…

A:

Q: psin z F(#) = [" t cos(t) dt (1) (a) . Compute F(T). Let

A: The solution are next step

Q: EXERCISE 6. dy +y dr where A is an arbitrary constant () - (+*) + A, Given that prove that tan

A: Solve By substitution

Q: Define T: (C¹ [0, 1], || · ||…) → (℃ [0, 1], || ||) by Tf = f'. Show that T is not continuous. Is…

A: T:C'[0,1], .∞→C'[0,1], .∞ T(f)=f' Let f(x)=xn then T(x)=nxn-1 T(x)=nxn-1 as n→∞,   T(x)→∞ So T is…

Q: Evaluate both sides of divergence theorem for A = pa, + pcos($)a+za, through the closed surface…

A:

Q: Q9. Find the value of the right side of Gauss divergence theorem for F = x²ī+ zī+ yz k over the cube…

A:

Q: 9. Find the bounds of integration a, b, c, d such that T (a, u) dydar. f(x, y) dædy =

A: x≤y≤4x=y →y=xy=40≤x≤4x=0 to x=4

Q: fx'e* dx ets

A: To evaluate:                     ∫x2 ex3 dx

Q: Evaluate the divergence of F = (exy, xy, z4) at P = (l, 0, 2).

A: Given  F=exy, xy,z4 at P=1,0,2

Q: Evaluate the integral.   ∫01 t cosh t dt

A: Given: ∫01tcoshtdt

Q: If f:[a, b] →R has a local minimum at p E (a, b) and f is differentiable at p, then prove that f'(p)…

A: