Use the Monotone Convergence Theorem (MCT) to prove the Nested Interval Property (NIP) (i.e. you need to prove that given a family of nested closed intervals {In = [an, bn]} there is an x ER satisfying an ≤x≤ bn for all n € N). [Hint: Use the fact that the sequence {an} is increasing and bounded above, by b₁ for instance, and then apply MCT.]

Q: Evaluate if x=4,8,3,-2 ∑x ∑x+1 ∑(x+1) 3∑x - 4

A: Given that  if x=4,8,3,-2

Q: Verify the following identities. Be sure to show all steps in a clear and neat sequence. 1. sin x +…

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Q: Simplify. Assume that all variables represent nonnegative real numbers. V49x"y" 17 ,7,17 | 49x' y"…

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Q: b2 over b-a + a2 over a-b

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Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: y" - y' - 12 y = e^(x/3)-e^(-x/3) A) Find the complementary solution of this homogeneous equation B)…

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Q: Express Ae-Ea/RT2/Ae-Ea/RT2 in the way that the number e only shows up once.

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Q: Add. -6+ 5+ (-4) (-2) || || ☐

A: Steps and explanations are as follows: When we see an expression like -6 + (-4), we can think of it…

Q: Remainder must always be either less than or equal to the divisor. true or false

A: Remainder must be either less than or equal to the divisor . The above statement is true .

Q: let B= [-1 2 7 -3] Find -3B

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Q: If a = [5,-2,1] and b.= [-1,-3,4], find | -a + 2b |

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Q: The table shows the movement of a stock for 30 randomly selected trading days. "Up" means the stock…

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Q: then A-1 A = -6 0 0 0 0 8 0 0 0 0 0 -5 0 0 0 -7

A: Consider the matrix

Q: Then show the classes that you used for display

A: First make frequency table in proper format:  Classes : ( define proper range )  Calculate…