State all integer values of x in the interval 1 2

Q: Use interval notation to represent all values of x satisfying the given condition. y = 7 -  | x/2 +…

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Q: Use interval notation to represent all values of x satisfying the given conditions: y = 1 - (x + 3)…

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Q: Prove or disprove: The inequality 1/(2^x) ≤ 1/(x + 1) is true for all positive real numbers x

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Q: Prove that the Intermediate Value Theorem remains true when the inequality sign is flipped, i.e.…

A: We know that According to Intermediate Value Theorem: A function is continuous in interval  I = [a ,…

Q: Use interval notation to represent all values of x satisfying the given condition. y = 1 - (x + 3) +…

A: y=1-x+3+2xy is atleast 4 i.ey≥41-x+3+2x≥41-x-3+2x≥4

Q: STION 16 implify the inequality z² + 2z < 15.

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Q: Prove that for x≠0 the inequality ex&gt;1+x holds.

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Q: Prove the following inequality, (1+x)^n>/= 1+nx+(n(n+1)/2)x^2, x>/=0 for any n>/=1

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Q: Find the supremum and infimum of the set x € R:x = +(-1)" ,n e N} + (-1)" ,n e N}

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Q: Show that if ƒ is both even and odd, then ƒ(x) = 0 for every x in the domain of ƒ

A: Given, function f is both even and odd function.

Q: Express the following statement using N-notation.: 12 (3x + 4) for all real numbers x > 2. x + 2

A: Consider the given statement.

Q: State all integer values of x in the interval [-1, 5] that satisfy the following inequality: 5x – 5…

A: 5x -5 &lt;-2      Interval -1 , 55x -5 &lt;-25x -5+5 &lt; -2+5         Adding 5 on both…

Q: use interval notation to represent all values of x satisfying the given conditions. y=7x-23+2(x+7)…

A: Given, y=7x-23+2(x+7) and y is at most 0

Q: The domain of g(x) = 3 consists of all real x - 2 numbers except 2, represented in interval notation…

A: Given :          g(x) = 3x-2 To determine :              The domain of g(x) interval notation

Q: Prove the inequality tanx2tanx1&gt;x2x1 provided 0&lt;x1&lt;x2&lt;π2.

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Q: a) Solve for x in the following questior 7-x = 1 %3D

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Q: Ifx and y are positive real numbers, use the direct method to prove the following inequality: Vxy s*…

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Q: Consider the set X = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X1, X2, X3, X4 = {0, 1}}. Show that x₁…

A: (a) It is given that x=x1,x2,x3,x4 such that 93x1+34x2+26x3+18x4≤131 and x1,x2,x3,x4∈0,1. So, the…

Q: express the set of numbers x satisfying the given condition as an interval.          I 4x - 1 I ≤ 8

A: 4x-1≤8

Q: Show that the equality [r + y] = [2] + [y] is not valid for all real numbers r and y.

A: Consider the provided question, We first define ceiling function. The ceiling function maps x to the…

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: x : x is a natural number less than 10​}

A: Write in explicit form

Q: State all integer values of x in the interval -3 3

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Q: o Yes, zero is contained in the interval.

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Q: Compute the following inequality   3x/(x2+2)-(1/x-1)≥0

A: Given,          3xx2+2-1x-1≥0

Q: State all integer values of x in the interval 3 -7

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Q: express the set of numbers x satisfying the given condition as an interval.       I 3x + 5 I &lt; 1

A: To solve the inequality: 3x+5&lt;1 Solution: We know that if x&lt;a then -a&lt;x&lt;a. We have…

Q: Prove the following inequality: п-1 Σ 3 k : k=[n/2]

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Q: State all integer values of x in the interval 1< x < 7 that satisfy the following inequality: -x + 6…

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Q: Prove that for x&gt;0 the inequality 1+2lnx≤x2 is true.

A: Inequality given in the question is: Consider the function; f(x) = 1+2ln(x)-x2 Let us find critical…

Q: Prove the inequality V1+æ – 1 –+ < 6 on [0, 0). 8

A: Consider the given inequality in the given interval. Use the graphical approach to prove the…

Q: Let ƒ(x) = x² + 2 x – 2. Find all the values satisfying f(x) < x² + 2. - NOTE: Enter an inequality…

A: Given f(x)=x2+2x-2

Q: Prove the inequality √1+x≤1+x2 for x&gt;1.

A: Consider the function. Find its derivative.

Q: Indicate the least integer n such that f(x) = (3æ³ + 2x²)(5æ5 + 4æ*) € O(x").

A: Finding f(x) explicitly using multiplication of polynomial. The highest power of x or degree of f…

Q: - Give the domain for k(a) in interval notation. x2 + 3x +2

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Q: State all integer values of x in the interval 3, 9 that satisfy the following inequality: 4x – 7< 11

A: Given : 4x -  7 ≤ 11

Q: For every real number x+1, n-1 1+x+x² +x' +. x´+x' +...+x" for all neN. 1-x

A: The question has a mistake , as in the R.H.S the power of x must be (n+1).

Q: let n be a positive integer not exceeding 20. How many values of n such that the equation x^2 +…

A: We have to find the values of n for which x^2+y^3n+1=1.

Q: The Intermediate Value Theorem can be used to prove that the equation x2 – x – 6 = 0 has at least…

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Q: Prove that for any positive numbers a and b the inequality ab+ba≥2 is valid.

A: It is required to prove for any positive numbers a and b.

Q: Prove Bernouilli’s Inequality which states: If x ≥ −2 then (2+ x)n ≥ 1 + nx for all natural numbers…

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Q: Solve the following inequality algebraically. Show your work on a separate paper. |x-2|29

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Q: Solve the following polynomial inequality. Express the solution set in interval notation. (x - 1)(x…

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Q: Find all pairs of consecutive even positive integers, both of which are larger than 5 such that…

A: We have to find all pairs of consecutive even positive integers, both of which are larger than 5…

Q: Prove the Inequality which states using  : If x ≥ −2 then (2+ x)n ≥ 1 + nx for all natural numbers n

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Q: The Intermediate Value Theorem can be used to prove that the equation 2²-2-15-0 has at least one…

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Q: Suppose also that P(X 2 8) = 3/4. Use Chebyshev's inequality to find a number u e R such that o u.…

A: Using the concept of Chebyshev's inequality, problem can be solved. please find step by step…

Q: 32 (c) Show that Hence, find the interval for x that satisfies the inequality = 22* 2 x 4" 32" -…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.