Consider f : N → N, g : N → N and          h : N → R defined as f(x) = 2x,g (y) = 3y + 4 and h (z) = sin z, ∀ x, y and z in N. Show that ho(gof) = (hog) of.

Q: 2. If J = [c, d), or J = (c, d], or J = (c, d) and / C [a, b], show that g =x, is Reimann b.…

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

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Q: Consider the functions z= -6 ex In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and as…

A: The given functions are z = -6ex lny,  x = lnu cosv, and y = u sinv. (a) The objective is to express…

Q: Consider the functions z =2e* In y, x In (u cos v), and y= u sin v. dz (a) Express and du dz as…

A: Since you have posted a question with multiple sub-parts, we will solve first two subparts for you.…

Q: f is not integrable on [0, 1].

A: It is given that f:[0, 1]→ℝ by f(x)=5x  if x∈ℚ0    if x∉ℚ We know, if lower integral and upper…

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A: Given, z=4exlny,  x=lnucosv,  y=usinv Part (a): z=4exlny,  x=lnucosv,…

Q: (e) If f(x) is reducible over Q then f(x +a) : a E Z is reducible over Q.

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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: 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: 4. Let f(x) = x, Vx E [0, b]. Show that f is integrable and that 62 f(x) dx : Answer:

A: Given function is  fx=x, ∀ x∈0,b

Q: Consider the functions z=7 ex In y, x= In (u cos v), and y= u sin v. dz dz (a) Express and as…

A: Given, z= 7 ex ln y    ....... (1)x= ln ( u cosv) .......... (2)y= u sinv…

Q: Find the local linearization of f(z) =z² at 9. lo(z) = %3D

A: Given : f(x) = x2   x0 =  9

Q: d x"J,(x)=-x"Jns(x) d, n+1 X.

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Q: Suppose that f(x) > 0 on [0, a], ƒ(x)< 0 on [a, b], ſo“ f(x)dx = 7, and S" f(x)dx = –3. Evaluate the…

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Q: 1. Determine whether f is Riemann integrable over (0, 1] and evaluate S f(z) dr whenever fE R(0, 1])…

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Q: Define f : X → K by f(x) = x'(1), x € X. Again, the linear functional f is not continuous. By 6.4,…

A: Given: f:X→K by fx=x'1, x∈X To prove f is not continuous using the given corollary.

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

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Q: Given n > 1, define f(z) = 1/z" for z +0. Show that f(z) = U(r, 0) + iV(r, 0) for cos(no) sin(no)…

A: We know that any point in the complex plane can be written in terms of polar coordinates in the…

Q: Let z = = g(x, y) = e* cos y +y In(x – 1).

A: Let we havez=g(x,y)=excosy+yln(x-1)If x=s-t and y=s2-t2

Q: 5) Determine the entire function f(2) = u+ jv satisfying Re(f(2)) = u(x, y) = ae" cos(y) + r? – y²,…

A: That's easy. Thumb up. Have a good day!!! We use Milne Thomsan's theorem

Q: Given F(x, y) = (e*y°(cos(x) + ¢(x)), 2ye*o(x)), with h E C'(R). then O (A) it does not exist o such…

A: According to our QnA guidelines, I can solve only one question .Please repost other question.

Q: Suppose f is Reimann integrable on [a,b]. If f (x)< 0 for all x E [a, b], then S f(x)dx

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Q: If U(x, y) = -e-Y sin x and f(x) = U(x, y) + iV(x, y) is analytic, then V(x, y) = Select one: O ey…

A: We have to find V(x, y) i.e.imaginary part of given analytic function,if we have real part is given.

Q: Suppose that f and g are integrable and that -1 f(x) dx = 5 h(x) dx = 4 7, dx = %3D Use the rules to…

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Q: 4. Show that the map K: [1, o) → [1, ∞0) defined by 1 t dt K(x) = 3 e 2 is a contraction in the norm…

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Q: Suppose w=x/y+y/z, where x=e3t, y=2+sin(t)x=e3t, and z=2+cos(6t). A ) Use the chain rule to find…

A: w=xy+yz, where x=e3t, y=2+sint &amp; z=2+cos6t Partially differentiating w=xy+yz with respect to x,…

Q: Prove that the function f(z2) defined by x*(1+ i) – y°(1 – 1) , (z ± 0) x² + y? f(z) = [0, (z = 0)…

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Q: 1. Show that the field F = (x + cos a)i+ (K +4 – y sin y)j + (2³ + K – 9)k is conservative and find…

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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 f : [0, 1] → R defined by if æ = 0, f (x) - L otherwise is Riemann integrable on [0, 1].

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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: 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: 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: Let f : [0, 1] → R be defined by f(x) : = x. Show that f ∈ R  [0, 1] and compute ∫^1_0(f) using the…

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Q: Let F(x, y, z) - z* + x+y sin x + x In z- 0, where z- f(x, y), then at (0,0,1) and are az %3D %3D…

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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 f(x,y,z) = x² sin y + y e, where x = t +3,y = net-1 and z In 2t. %3D %3D at t 1 is: dt -2 O None…

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Q: Suppose that f and h are integrable and that: L f(x) = -1, f(x) dx = 5, h (x) dx = 4 , Find: %3D %3D…

A: Answer and explanation is given below..

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

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Q: Use Stokes's Theorem to evaluate F dr, where F(x, y, z) = x²i+z²j-xyzk and S is z = /169-x² -y² .…

A: As per our guideline we can't use any computer algebra. I calculate both line integral and surface…

Q: Let Juce) 2ntv () %3D A=O n!F (I+u+n) Bessel function Of the first Kind be a Of Order V Show that…

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Q: Expand the function f(x) = tan x up to the first two non-zero terms in the Taylor's polyno- xn+1…

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Q: Given F(x, y, z) = (tan y + cosh x Joi 2xy)i + (x sec² y - x² + 1)ĵ - 2zk, evaluate F. dR where C'…

A: Given that,  F→x,y,z=tany+coshx-2xyi^+xsec2y-x2+1j^-2zk^, Therefore, set fx=tany+coshx-2xy…

Q: Suppose that f is continuous on [0, 1], ƒ(0) = 0, and f'(0) exists. Prove that the Lebesgue integral…

A: This is a question of measure theory.

Q: Consider the following theorem. Theorem If f is integrable on [a, b], then FX) dx = lim ° fx;,)ax n-…

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A: The objective is to find the derivative.

Q: Consider the following theorem. b - a If f is integrable on [a, b], then f(x) dx = lim n- 00…

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