What is the interval of convergence of (х — 3)" n n=1 O a. I: (-1/2, 1/2) O b. I: (negative infinity, positive infinity) O c. I: (a) = 3 O d. I: (2,4)

Q: which of the following intervals is f(x)=1/sqrt(x) not continuous? Explain how you arrived at your…

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Q: Express f(=) = in a series of positive and (: – 1)(:– 3) negative powers of (: – 1) -

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Q: (13) Prove by induction that for each whole number n, 1. You may use the fact that for each whole…

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Q: Evaluate fr.co x cos(x³) dx as an infinite series.

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Q: Find P (-1.5 < or equal to Z < 0.2) where Z ~ N (0,1)

A: We will use Standard Normal table to find the required probability.

Q: Prove that x² + ¹² +2111²2 = y 1112 where prime denotes differentiation w.r.t.s. 1 1+p¹² 4 p² o² + P

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Q: ∞ Use the series reine, for some 0 <r < 1 and 0 € R, to show that 72=0 Erm cos no 7=0 1r cos 0 12r…

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Q: Find the intervals on which the function is continuous. x +5 17) y =2-7x + 10

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Q: 8. (13 points) Define f: ZZ by f(n) = 5n - 5 for all integers n (a) Is one to one? Prove or give a…

A: Step 1:Step 2: Step 3: Step 4:

Q: (a) Let the interval a, b be divided into n equal sub-intervals such that a = x0 < a1 < x2 < x3…

A: From this general formula we can obtain different integration formulae by putting n=1, 2,3 etc. We…

Q: Find the interval of En=o 2"(z – 3)" O (3.5, 0) O (2.5, 0) O (2.5, 3.5) O (2, 3)

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Q: 5. (a) Verify that t(n) = t(n+ 1) = t(n + 2) = t(n + 3) holds for n = 3655 and 4503. (b) When n =…

A: To find-  Verify that τn = τn+1 = τn+2 = τn+3 holds for n = 3655 and 4503 When n = 14, 206, and…

Q: 03. Use Taylor series ( use a=1 and n-1) to evaluate the following: sin x-x+x' a) lim b) " de

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Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

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Q: Euler's Tution function: (n) is the number of positive integers less than n that are relatively…

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Q: Siven the following: 00 5(-1)"x2n '(-1)"x²n cos(x) = for all x E R (2n)! n=0 ) Find a power series…

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Q: Which of the following does not satisfy the conditions of the Mean Value Theorem on the indicated…

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Q: 22) which of the following functions is uniformly continuous on the giuen set? a) flx)= x 3 on 10,1)…

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Q: Suppose that Z~N(0,1). Then find Pr(2.78 < Z < 2.84)

A: Given data, Z~N(0,1) That is Mean=0 Standard deviation=1 P(2.78 &lt; Z &lt; 2.84)=?

Q: 2. Let f be the arithmetic function defined by f(n) = (-1)". Compute Z;(2) = f(n) n2 n=1 Hint:…

A: Solution: We will use the following formula Here n0=2

Q: te the Taylor series for f(x) = S

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Q: Prove the follawing identities. 4-V. 4- V = AV (a) (b) M8 = A/1+ 4) (1+ A)" 2. (C) 4/f = I for Afn-…

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Q: The function h is given by h (x) = |. (2+2 1n (In t) – (In t)) dt for 1.1 1.1 < x < 7. On what…

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Q: 15 Let (x+1) {x-2}" 20 g"k) = concave upX-) on what interval(s IS (NOte: Crinen gil but aske about…

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Q: ind the half range CoSine Series for the function(x-1) tn the Intervat Henfe that くX<t ++ 32

A: Since you have posted multiple questions but according to guidelines, we will first question for…

Q: onal the (i) Int(A) (ii) (A) and A (iii) Whether or not A is open or closed.

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Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…