Aち=N: 5k Question 3 [$2 Q7] For every positive integer n, suppose S, = [n - 1, n) the right-half open interval. Show that (a) U S, [0, o0); (b) Sn = 0. |3D %3D n=1

Q: Let f (x, y) = 1 5+√x²+y²-1 Then range of f is:

A:

Q: Consider the graph of y = x² on the interval [-2, 2]. Using 2 rectangles of equal width, give the…

A: Find the lower sum of f(x) with 2 rectangles

Q: 4. Let f(x) = 4x22/3-19x71/11 Determine the largest n for which f E C". %3D

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Q: If you were asked to find R6 on the interval [4,10], what x values would be evaluated? 5,6,7,8,9,10…

A: To find R6, we partition the given interval [4, 10] into six equally spaced sub intervals.

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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: Show that when |z +1| < 1,z² =1+£(n +1)(z+1)" n=1

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Q: Find a one-to-one correspondence between [0, 1] and (0, 1). Find a one-to-one correspondence between…

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Q: Let a and b be non-negative real numbers with b+ 0 and p,q > 1 and+= 1, then a show that ab <+

A: Define a function y : [0,∞)→ℝ by yt=1q+tp-t1p, for every t∈ [0,∞). Now differentiating,…

Q: A ˅ B => C ˄ D   into conjunctive normal form by using equivalences

A:

Q: X1 X2 X3 S2 R.H.S 1 9-0 11-20 7/30| 24-30 X1 1 6. 2/3 -1/6 6 X2 -1 -1/3 1/3 12 a) O<O9 b) O<O520/3…

A: Remark: Optimality condition for Simplex method:  The Optimality condition is reached at the…

Q: (3c) Let n E Z. Prove that if n is odd, then 4|(n² – 1)

A: here is the proof

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Q: Show that there is a correspondence between the two intervals [0, 1) and [0,1].

A: Given interval 0≤x&lt;1 is a subset of  0≤x≤1. In this situation ,there is an obvious injective…

Q: 2n2 Using the mean-value theorems, show that in sin z w/6

A:

Q: If Z~N(0,1), then what is Pr(-0.09 < Z < 2.54)? You can use Excel. Enter your answer as a decimal…

A: We have to find given probability

Q: - (10 points) Show |a – b| < |a| + [b| Va,b eR.

A: We have to show that  a-b≤a+b      ∀a, b∈ℝ

Q: Show that the nondegenerate interval [2, 5] is uncountable.

A: Here first we have to show that  is not countable.If possible let,  is countable ,so A can be…

Q: Show that x + is increasing on [1, 0).

A:

Q: let XnN(20, 0136) iF P(X<M) = 0.05 then the value of mis

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Q: Let x and y be positive real numbers. Prove that a + y > 2/xy.

A: See solution below

Q: (a, 0) is not measurable.

A: In this question, we check the given set is measurable or not. here we use the condition of Lebesgue…

Q: DeMorgan's theorem states that Select one: a. (A + B)' = A' * B b. (AB)' = A' + B' c. A' + B' = A'B'…

A: We are given some statements to verify De Morgan's theorem. We can do this in the following way:

Q: Find a nonzero vector in Nul A and a nonzero vector in Col A. -5 -2 3 0 -1 A -2 -2 7 2 -1 0 -5

A: Given A=-5-23-10-10-2-2-572   To Find: a non-zero vector in Null(A) and a non-zero vector in Col(A).

Q: Define f: N→ N by f(n) = 2". Find range(f).

A:

Q: 4(-1)" Σ 3) Estimate 2N 1 correct to one decimal place. N-1

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Q: Evaluate Hint: Use differentiation to show that n=1 (1 – x)-2 = nx"-! (for |x| < 1)

A: We have to show that 1-x-2=∑n=1∞nxn-1