Find g: R R, continuous in [0. ) and position in (0, ) satisfying g1) %3D )dt

Q: If f is bounded and integrable on [a, b] such that | f(x) | 0).

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Q: The function f(z) =e² is: u(x.y)=e*cos(y) o u(x,y) =e*sin(y) ¤ contiuous in СО discontiuous in CO

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Q: 2. Let f and g be integrable functions such that f(x) dx = 6 and g(x) dx = –2. Using the Linearity…

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Q: e In (xle ) (2– sec²x) sec(3A – x) sec³x dr What should be the value of A for to be integrable using…

A: integration by substitution method

Q: Find the singularity of the function f(z)=(e^z-1)/z at z=0.

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

A: Given :

Q: Let H(x) integral ,for -2 ≤ x ≤2.Find the value of s such that H(x)= sH(-x).

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Q: If f is bounded and integrable on [a, b] such that | f(x) | 0).

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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: 10. If f(z). g(z) is integrable on [a, b). prove that (z)g(x)dx f(z)dx g(x)dr.

A: Given that, f(x),g(x) are integrable on [a,b]. The aim is to show that…

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: If f is bounded and integrable on [a, b] sch that | f(x) | 0). 9.

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Q: Let f be the function defined by S1+x, when 0<x<}, }<x<1 0, when x-1. f(x)= Show that fis integrable…

A: Recall the Result/Theorem A bounded function f which has only a finite number of points of…

Q: If f is bounded and integrable on [a, b] such that | f(x) | 0). a

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

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Q: Evaluate the integral, if it exists.

A: Given: ∫-π4π4t4 tant2+costdt

Q: f(z) =|z| is continuous in C 0 صواب ihi O

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

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Q: If f is bounded and integrable on [a, b] sch that 1f(x) | 0).

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Q: Evaluate the integral | t(sec t2)4 dt

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Q: Compute d/dt f (r(t)) at the given value of t for f (x, y, z) = xz − y^2, r(t) =〈t, t^3, 1 − t〉at t…

A: Given: The function fx,y,z=xz-y2and rt=t,t2,1-t, To find: ddtfrt at t=-2,

Q: (a) Compute f(t)dt. (b) Compute the total area between and the x-axis over the interval YA y = f(t)…

A: We have to find the total area according to the given information

Q: Find the weighted integration norm (f, f) = | f(x)f(x)w(x)dx of the given polynomial on C[0, 1].…

A: Norm of a vector is defined as f=f,f.

Q: Find the first order moment of pdf f(x) = (X^2)(x)[e^(-^x)], x 2 O, and O elsewhere. O /2 2/A O…

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Q: If f is bounded and integrable on [a, b] such that | f(x) | 0). a

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Q: If f is bounded and integrable on [a, b] such that | f(x) | 0).

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Q: Let / = [c, d] [a, b], show that g =xj is Reimann integrable on [a, b] and b. S g(x)dx = d-c a

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

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Compute the Wronskian of a set of functions {vı, y2} = {e* cos(/), e* sin(v¤)} cos (Væ), e* sin(va)}…

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Q: Evaluate the integral f (t* In ti+ 3t° sin (t*) j + ) dt. (x+1) -2

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Q: Use the local linear approximation of (1 – x)2º at xo O to estimate (0.99)2º. %3D

A: The linear approximation of f(x) at x0 is given by L(x) = f(x0) + f'(x0) (x-x0)

Q: (a) Let Ty if +y +0, g(x, y) = 0 if r = y = 0. Prove that g(r, y) is continuous at (0,0).

A: To Prove: g(x,y) is continuous at (0,0)

Q: Let H(x) integral ,for -2 ≤ x ≤2.Evaluate H(0).

A: Consider the given integral, Hx=∫0x4-t2dt use the substitution method to solve the above integral as…

Q: If f is bounded and integrable on [a, b] such that | f(x) | 0). *0).

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

A: The solution are next step

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: Express the antiderivative F of f satisfying the given initial condition as an integral. f (x) = sec…

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Q: Define f : [0, ∞) → [0, ∞) by f(x) = Vx. (a) (b) Prove that va +b 0. Prove that f is uniformly…

A: We have to prove that   √a+√b≤ √(a + b) for all a, b ≥ 0.

Q: Let g(x) 8 In(t) dt. Use the Fundamental Theorem of Calculus tc g'(x) =

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Q: Assume x and y are functions of t. Evaluate dy / dt for 4xey = 8 - ln 64 + 6ln x, with the…

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Q: If f is bounded and integrable on [a, b]such that | f(x) | 0). *0).

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Q: The joint PDF of X and Y is given by f (x, y) = x+ 0 0 and y E (0, 1), derive E[X | Y = y] in terms…

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Q: Check the following bound under the assumption of independence and dependence tPy 0.

A: Given: Under the assumption of independence and dependency, check the following bound,…

Q: Assume x and y are functions of t. Evaluate dt for 4xeY12-In 729+61n x, with the conditions -6, x-3,…

A: Given that 4xey=12-ln729+6 lnx and the conditions are dxdt=6 , x=3, y=0  find dydt

Q: Find the weighted integration norm (f, f) = | f(x)f(x)w(x)dx of the given polynomial on C[0, 1].…

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Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following .xey = 2 - ln 2 + ln x;…

A: It is given that, therefore the time derivative of the given function is, But it is also given…

Q: Suppose that f is integrable and that f(z) dz = 3 and Si f(2) dz = 7. Find Ги a. f(z) dz b. f(t) dt

A: Given: Using identities:

Q: ) Let f(x) = cos(x) ln (1+ ax 1+bx, 1 1 2'2 If f(x)dx = 0 where a and b are real be integrable on…

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