I. Find the length of the following sets: 1. e((-0.1,1.5)) 2. P(R) 3. e((-∞,4]) 4. e((4,7) U [7.1,7.95)) 5.

Q: 2 = 1+ 2i 2- i and w = what is z + 3w ? a. 7+i C. 5+ i b. 7-i d. 5-i

A: Solution

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Q: 1. Let f(x,y) = x² + y², g(t) = (3t+1, 2t − 3), and F(t) = (fog)(t). Evaluate F'(t) both directly…

A: 1. Given,              f(x, y)=x2+y2, g(t)=3t+1, 2t-3 and F(t)=f∘gt.

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A: We have to solve given problems:

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Q: Suppose (Zn)-1 CC and for each n € N+, let zn = xn+iyn, where an, yn E R. Suppose z = x+iy, with r,…

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Q: (i) Prove by mathemarical induction on n that 3" > 2n² + 1 for all n € N (ii) Given the function g :…

A: "Since you have asked multiple questions, we'll solve the first question for you. If you want any…

Q: 2. a) Find an example of a real valued function f:R +R and SCR so that S is open while the forward…

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Q: L ·∞ x¹/3 −1+x5 dx

A: Given: Here is the given, ∫-∞0x13-1+x5dx To find: Complex analysis.

Q: (a) Find the following limits (i) lim (v/2n + I – v2n) 3n –n+8 lim- 4n(n – 1)(n – 2)

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

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Q: 4. Use the inequality | sin r|< |x| for x E R to show that the sine function is continuous at r = 0.…

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Q: Let n € N. Use the rational roots theorem to prove that √ is rational if and only if it is an…

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Q: 2. a) Let f be absolutely continuous on [a, b]. Will the function |f| be absolutely continuous on…

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Q: 6. Let X be a metric space. Let f: X → R and g : X - R be real-valued Lipschitz functions with…

A: We have to solve given questions.

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A: Given: Indirect method of proof : given if A is true then B is true.

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Q: Problem 2. Let p be a real number such that 1 0, and the function Tf is continuous on 10, ∞[ and…

A: Given information:Let us consider the given operator T,(Tf)(x)=1x∫0xf(t)dtTo prove:The operator T is…

Q: 4.) Let f(z) be an analytic function. Show that the following equality is hold. %3D

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Q: Let A and B be non-empty sets of real numbers with inf(B) = 2 and sup(A) = ; Then sup(2A – 3B)…

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Q: linear algebra

A: 6. The given matrix is

Q: 1:1:2•: 3:1:4:|'5|:6:1:7:1:8.1 9.1 10: I 11: |·12: | •13• T 14: 1·15: |·16· I 17. I 18. | • 19:…

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Q: Problems: (1) If f and g are continuous at x,EDf ). Prove that f +g is continuous at x..

A: I have used the apsilon delta definition. It also possible to prove using sequential one.

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Q: Question 1 Prove the limit comparison theorem i. Suppose that an20 and b,20 and that an lim 7= Then…

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Q: Suppose f,9 : D R are continuous on D. uniformly continuous on D. Prove that f +g is uniformly

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Q: (3) (a) Let T be a surjective linear transformation from P7 W. Show that dim(W) dim(W). Lastly, the…

A: Given below the detailed solution

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