Let an m be non-negative numbers for all integers n, m > 0. Deduce Ši an,m = ΣΣ An,m n=0 m=0 m=0 n=0 as an appliçation of Fubini's theorem.

Q: For each n ≥ 1, take An= (-1/n, 1/n). Then, 1 An {0} and U1 An (-1, 1). Prove these.

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Q: Let Z~ of Z N(0,1). Find Pro.1 Select one: a. 0.81 Оъ -0.81 O c. -0.44 Od 044

A: We have given that  X~Normal(mean=0 , standard deviation=1) Find Z-score  P(Z<z)=79.1%

Q: Suppose that q 1 is a constant. Calculate the sum n Sn = kqk = q + 2q² + 3q³ +…+nq” k=1

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Q: Suppose ū = 2j + k, ū = 2i – 4j + 2k and w = -5i – j+ k. %3D Compute the following values:

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Q: Let Sy := {1-(-1):NEN. Find iNf Sy and sup Sy

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Q: Let y1, . ... Yn real numbers, and let n y = 1/√ Σ² ²=1 Yi n their arithmetic mean. Show that for…

A: The proof is explained in the explanation section.Explanation:Solution: Let's prove the given…

Q: (a) Fix any positive integer n. Use logarèthmic differentia Hon to find fn (x). b) Find the smallest…

A: a For each posotive integer n, define a function fn by settingfnx=∏k=1nxk+1 , x∈ℝ…

Q: Prove 2- = =4 has infinite many Solu thans ZEC.

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Q: Evaluate dx V In(8-x)) at x = 1. = 1.

A: We have to find: ddxln(8-x2)3   at x = 1.

Q: Show that if a, = (a" – B"), where a = (1 + v5)/2 and ß = (1 – V5)/2 , then th An = an-1 + an-2 and…

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Q: 'ind integers s and t such that s · 35 +t · 78 = 1. Show your work.

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Q: Find the singular values σ₁ ≥ σ2 of 01 = 02 -1 -27 A = -2 1 -2 2 9.

A: Find the singular values σ₁ ≥ σ₂ of the matrix A: Singular values of a matrix are the square roots…

Q: If S:= {1/n - 1/m²n,mEN }, find inf Sand sup S.

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Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x :x > 5}. Find h. D'n (AUB)

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