Prove that for x > <1+ ax, if 0 < a < 1, 21+ ax if 1 < a <∞o.

Q: 2. Let x1x₂ >. (1+x₁) n . xn> 0 ben real num 1 + x₁ + x1x2 + .. + x1xz

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Q: Assume that 2< a < 3 and1<b< 2. Prove that: 2 < a? - 2 < 8. VI

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Q: find a Positive integern for which the equality holds %3D

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Q: 49. Prove that x +> 2 (x1/2 – x-1/2)2. 2 for all x > 0. Hint: Consider

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Q: d) Prove that −1 < x < 0 implies that |x³ − 2x + 1| < 1.26|x − 1].

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Q: For each of the statements below, give a domain of discourse for which the statement is true, and a…

A: Part(1): Given, ∀x∃yy2=x x≥0 then the statement is true Therefore, x∈[0,∞) If x&lt;0 then the…

Q: Which x satisfies both Ix - 31 &lt; 2 and Ix - 51 &lt; 1?

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Q: find lim (2 x3 - 3 x + 5) X --> -1 O 6 O none of these answers O 4

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Q: b) Prove that |x| ≤ 1 implies that |x² + 2x - 3| ≤ 4|x − 1].

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Q: Find g(-T" 1+h -)-2 for h<<r r

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Q: Let & € N. Prove by using the contra-positive that if ³ is odd then x is odd. Proof: Choose the…

A: Introduction: Contra-positive method is the way to prove a mathematical statement. Every conditional…

Q: If Xo and X, are two numbers with Xo F(X1) O B. F(XO) = F(X1) O C. None of the above O D. F(X0) <…

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

Q: Find a number n e N such that 2" > 102000 and 2" has among its 2000 last digits at least 1000…

A: We will use logarithm to solve the problem

Q: |x=1| 1 lim x+1 X-1 A True B) False

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Q: Prove a^2 +4a+3 is odd if and only if a is even.

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Q: Indicate the least integer n such that (3x5 + x²)4 = 0(x¹). E

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Q: Which of the following sets is empty ? * O (x: X = x*2} O (x: x is not equal to x) O (x: x is not…

A: A set is said to be empty if it does not contain any element.

Q: 2. Transform this LP into its DUAL counterpart. min 3x, + 2x2 - X3 subject to X1 + x2 = 5 -1 < x, <…

A: Transform this LP into its DUAL counterpart. Our problem can also be viewed as,   MIN  3x1 + 2x2 -…

Q: In 3 - In x - In(x + 5) = 0

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Q: 8) lim 2ex+1 xx ex+1

A: Ans :

Q: Use proof by contradiction to show that there is no positive real number x such that (x-2)/x ≥…

A: In an inequality, if a positive number is multiplied then there is no change of sign of inequality.…

Q: (-5x + 4, for x 2 |1, Evaluate fl-1) - f(5)

A: Using the given function f(-1) = (-1)2 +3 = 4 f(5) = 1

Q: Prove that for every real number x, 3x - 6 ≤ x iff |x-1| ≤

A: The objective is to prove that , where  is a real number.The inequality  is equivalent to .

Q: Which of the following statements below are true for f(x) = - 2(x - 1)(x - 2)(x + 3)(x + 4)? * i) as…

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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: Prove that 1¹x 2² x 3³ x...xn" < n(n+1) 2 (2n+1) 3

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