20. Use forward reasoning to show that if x is a nonzero real number, then X + 1 > 2. [Hint: Start with the inequality (x - ) >0, which 2 holds for all nonzero real numbers x] Mention the method that is used.

Q: 4. [5] Please find in interval notation the values of x for which this expression is real. Show…

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Q: Prove (kindly provide reason/s) that for any real numbers m and n, (-m) + (-n) = - (m + n)

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Q: Solve the following inequality graphically in two-dimensional plane: x > – 3

A: We first draw the line x=-3

Q: solve the following rational inequality (x)/(1-x) <=3

A: To identify all the real numbers x satisfying the given rational inequality

Q: Prove by contrapositive: if x is odd then x²+3x+5 is odd

A: Concept: Contrapositive method: A conditional statement's contrapositive is built through negating…

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: 14. Demonstrate that 21 has no primitive root.

A: An integer n≥2 has a primitive root if and only if the the number n is one of the following; 2,4,…

Q: Prove that the K4 is not consecutive.

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

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Q: Is there a real number that is bigger than all integers? If so what is the number and if not what…

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Q: Use direct prove to prove that for any two positive numbers x and y, Vxy s*+y 2

A: Suppose x and y are two possitive integers.To show: xy≤x+y2  since squares are always positive,…

Q: 8.26 Show that the IVP x" = –6x(x')³, x(-1) = -1, x'(-1) = , has a unique solution x and find the…

A: Given IVP is x''=-6x(x')3 , x(-1)=-1 ,x'(-1)=13

Q: 6. Show that Vz eC i) z-7 is a real number. ii) (z-2) is a real number.

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Q: Suppose that ƒ(0) = 5 and that ƒ'(x) = 2 for all x. Must ƒ(x) = 2x + 5 for all x? Give reasons for…

A: given: f(0)=5 f'(x)=2

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

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Q: + Prove that if a is a nonzero real number, then 1. 25z? 1 (Hint: Start with the inequality (a - 20,…

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Q: 9. Prove that there are as many positive real numbers as there are real numbers.

A: Consider the set X and Y. Then we said that |X| = |Y| if there exists bijective function from X to…

Q: Prove by contraposition If a sum of two real numbers is less than 50, then at least one of the…

A: To prove the required statement by contradiction

Q: (4) Prove that there is no smallest positive real number.

A: I have to prove that there is no smallest positive real number . Suppose that there is a smallest…

Q: Prove (kindly provide reason/s) that for any real numbers m and n, (- m ) + ( - n) = - ( m + n)

A: To prove: -m+-n=-m+n Where m and n are real numbers.

Q: 6. Show that the half open interval [0, 2) is uncountable. (Hint: We know that (0, 2) is uncount-…

A: Since the interval (0, 2) contains the infinite subset {1.2,1.3,1.4,...} So (0, 2) is either…

Q: Show work to justify your answer. Which of the given values will make the inequality n-93 > 175…

A: Given that the inequality is            n - 93 &gt; 175 Here we have to find for which values on n…

Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

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

A: Given data:     The given inequality is: . The given expression can be written as, Here, f(x) is…

Q: Suppose x and y are positive real numbers. If x< y, then x² < y².

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Q: 27. Show that if x and y are positive real numbers that have the same first n digits in their…

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Q: s) Express the infinite contimod fraction [2, 1,5 quadratic irrational- as a ity.

A: We need to express the infinite continued fraction 2, 1, 5¯ as a quadratic irrationality. The…

Q: Prove in a thoroughly written proof that for all integers a  and m, if a and m are the lengths of…

A: Recall the following. Pythagoras theorem: For any right triangle, the square of the hypotenuse is…

Q: 3. Show that (5+ 13)e + (5- i3)-" is a real number if is also a real number.

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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: Indicate for which natural numbers n the given inequality is true. Prove your answers by induction.…

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Q: Find the smallest k such that the following inequality holds true: 2* + 1000 < 3k+ 100 < 4k

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Q: Show how to adapt the proof that v3 is irrational (from the video) to prove that v15 is irrational.…

A: 3 is irrigational number: Let 3 is rational number then 3=pq,where p, q are both integers and q≠0…

Q: 6. Suppose x is a real number for which x2 is irrational. Use a proof by contradiction to prove that…

A: Contradiction method means, If we want to prove If P implies Q, Then we are first assuming P and…

Q: 2. Let x be irrational real number. Prove that 2x+3 is irrational

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Q: 5. IS the following statement TRUE or FALSE? If the statement is true, prove it, and it is false,…

A: Introduction: The biggest integer function (also known as the floor function) .:R→Z of a real number…

Q: Show that the interval [0, 1] is uncountable.

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Q: (b) Prove that 2m ≤ m! + 2 for m ¤ N. (c) For any nonzero real number x, prove ---3 i=1 = 1- x -n

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Q: 8) Find what va lues of x salisfy the fellowing inequality: 3x -1 >2 2x +5

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Q: 3 By applying the Intermediate Value Theorem choose the interval over which x4 = 7x3 - 5 will have a…

A: The given problem is to find the interval for the given function that which the intermediate value…

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

A: To Prove: Bernoulli's Inequality which states: If x≥-1, then (1+x)n≥1+nx for all natural numbers n

Q: What is the contrapositive of the statement “ A rectangle R with side lengths 1 and x, where x is…

A: theory Indeed, the ratio between length and width must be rational, even if we don't require the…

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 sum of any positive integers that is less than 30

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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: The Archimedean Property says that the set of real numbers have no upper bound. True or False

A: Given a statement , we have to check whether it is true or not. As we know the property of…

Q: Enter a counterexample for the conclusion. If x is a prime number, then x+1 is not a prime number. A…

A: Prime numbers: The numbers which are divisible by 1 and by itself. The given conclusion is that if x…

Q: "8 does not divide x^2– 1 if x is even". prove it directly

A: We need to prove  8 does not divide x2 - 1 , if x is even. OR if x is even, the 8 does not divide x2…

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…