Riemann integrability to

Q: ction of f(A) = when -1 w) where w>0

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Q: x if 1<x < 2 4 - x if 2 <x < 3 Q1. Let f : [1,3] +R is given by f(x) = %3D (a) Show that f(x) is…

A: Since the given function f is continous on a compact set [ 1, 3 ] which implies that it's image is…

Q: y" - 6y' + qy 2,

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Q: Show that 2f E R[a, b] and | [2f(x)] dx = 2 e| f(x) dz. 2.

A: We solve this problem  using Riemann integration . The complete solution in the next step .

Q: Solve if w be cube root of unity then (1+w)(1+w^2)(1+w^4)(1+w^8).....2nfactor=1

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Q: 2) P(V,T) = "RT (assume the number of particles/moles n is constant)

A: write down the total differential of the following function P(V,T) = nRTV.

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

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Q: f (x) = -x² + 5æ, [0, 5]

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Q: y" +2y' = 3+ 4 sin(2t)

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Q: Verify Stokes's Theorem for F = z²î + x²j + y?k and S is the surface z² = x2 + y2, y 2 0, and 0 szs…

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Q: Radius of the earth: 6378 km Mass of the earth: 5.9767 * 1024 kg Mass of the sun: 1.991 * 1030 kg…

A: We will find out the required value.

Q: P(x1, x2) = x1X2, Q(x1,x2) = –2x102; D = {(x1,x2) :1 < x1 < 2,0 < x2 < 3}. %3D

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

Q: Find all point of discontinuityz is a complex variable, z=x+iyf(z)=(1/z)-sec(z)

A: To analyze the behaviour of the given function of the complex variable z.

Q: Using only the definition of RS-integral, evaluate 2 d[x}.

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Q: Continuous everywhere

A: The following are theorems, which you should have seen proved, and should perhaps prove yourself:…

Q: Underline the domain and then write the negation of the following For all real numbers x, if sin(x)…

A: We know the sin function very well. Graph of the function is  Since the sin(x) is periodic and we…

Q: lim [ln(1 + x²) − ln(1 + x)] - X

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Q: 2 € C: |Re 2| < 2 < 2

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Q: Question 7: Evaluate v² dv (Reimann Method)

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Q: If f(z) dr = 2 and I f(z) dr = -3, then (3f (x) + 2) da = %3D

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Q: Let F be the vector field F(x,y, z) yzi + xzj + xyk and C the ellipse given by r(t) = 5 cos t i+…

A: Given vector field: Fx,y,z=yz i+xz j+xy k The ellipse C is given by: rt=5costi+3+2sintj…

Q: f(n) = 2f(n – 1) +n² for n > 1; f(0) = 1. %3D -

A: According to our company policy, I am supposed to answer only one question at a time. For the rest…

Q: Compute 25200 mod 27.

A: As 25 is coprime to 27, by Euler's theorem, we see        25φ(27) ≡ 1 (mod 27)  Now,        φ(27) =…

Q: Use the Cauchy-Riemann equations to show that f(z) = z is not analytic.

A: A function is said to be analytic when Cauchy-Riemann equations are satisfied. The Cauchy-Riemann…

Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line…

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Q: 2. Let S denote the surface of the cube [0, 2] x [0, 2] x [0, 2], but with a small square removed,…

A: Let  denote  the surface of  the  cube but with a small  square removed, the  square with corners…