Which of the following statement is always false? (a) For all integer x, [x] = [−x] (b) For all odd integers x, 11] =*2¹ (c) For all real numbers x, [xy] = [x][y] @Q All the above

Q: b) 4(x – 4)(x + 2)² (2x – 1)³ < 0 - -

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Q: In(x²) = 2 ln(x) for all x True O False

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Q: (4) Prove in two different ways that if a is a positive r number, then (a + 1)" > a" + na"-1:

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Q: (c) Prove that r| +11 36 T-1 2 +36 for all real I.

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A: Given that  an=2nan-1, a0=3 To find the solution of this recursive relation

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A: Solution:

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A: It depends on the conditions; If F is a increasing function then option D is correct. If F is…

Q: Prove an+1 = (an2+ 1) / 2 with a1 = 2 is monotonic increasing.

A: Solution:-

Q: Evaluate each of the following for x = 5, 7, 9 and 2. ∑x2 ∑x2 – 5  ∑(x2−5) 2∑x2- 5  2(∑x2- 5) 2)

A: Given:   X = 5, 7, 9, and 2.

Q: 2) + 2 <0 IX + 31 4,

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Q: x2- 11x+24 For all x 8, = ? ? 8-X 8-X 3-x X - 3 X-8 K X - 11

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Q: If Xo and X, are two numbers with Xo < X, then the true one is

A: Answer:-  Option D is the correct answer.

Q: (c) Prove that x - 11 |x| + 11 |x² + 36| 36 for all real r.

A:

Q: If a, b, c are non-zero real numbers, then bc ca ab ca ab bc vanishes, when ab bc ca ca 1.1 -+- 0…

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