2. Let x be a real number. Prove that for every e > 0 there exist two rational numbers q and q' such that q< x < d' and q- q' < €.

Q: +12x+19 in the interval [-1,6] of the above no zeroes in the interval [+1,6] 5 zeroes in the…

A:

Q: 2. Determine all values of x for which 0<= x2-11/x+1<=7 (include graph and intervals tables) *in…

A:

Q: *2. Let x and y be distinct real numbers. Prove there is a neighborhood P of x and a neighborhood Q…

A:

Q: 17. The interval for function Is+3|2 1/2 is (-7/2,- 5/ 2] 0(-7/2,-5/ 2) (-00,-7/2)u(00,-5/2)…

A: Given: s+3≥12 We have to find the interval in which the given inequality satisfies.

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

A:

Q: Let X~N(10,9).

A: The mean of the distribution is 10. The standard deviation of the distribution is 9.

Q: 2. Statement such as a < a is an example of: Function Equation Expression O Inequality

A: Inequality: An inequality is a relation which makes a non-equal comparison between two numbers or…

Q: Show that for all x>0, e* >1+x+÷ 2.

A:

Q: Q1. How many pairs of ordered numbers exist such that their sum, product, and quotient are the same?

A: Keeping a note, according to our guidelines we can only answer one question, kindly repost other…

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

A:

Q: Show that it is not true that for every error 1/m there exists n such that |Ek=1 polt – r/(1 - r)| <…

A: We will show that for every m there does not exist any unique n that works for all r in (0,1)

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

A:

Q: (b) y'(t) — 4y'(t) = 24 cos 2t_y(0) = 3, y'(0) = 4

A:

Q: 19. The real number k lies between 0 and 1. The area of the quadrilateral formed by the lines y =…

A: The objective of the question is to find the area of the quadrilateral formed by the lines y = kx, y…

Q: 9. Find a pair of positive integers a<b such that a+b=557685 if possible. Ans:

A:

Q: Seaet =1+ e* + e3x + e(n+1)x enx +esx. n! sx € (0,e*) | ... 2 (п + 1)!"

A: we know that ex=1+x+x22!+x33!+........................+xnn!                      ..1

Q: Find the domain of f(x)= Mostly sunny x|x€Rx‡¬ √10} 00 x|x€R_x#√10} Ox|x€R¸x*-√√10, 10}…

A: a2 - b2 = (a - b)(a + b)  and 10 = (10)1/2(10)1/2

Q: 10. Evaluate | x In(x+12) « dr.

A:

Q: Let X~ N (24, 49), Find P( 10<X< 38)

A: Given sample are: 24, 49 Mean of these samples are: μ=24+492=36.5 Standard deviation:…

Q: 7. Find a pair of integers (x,y) such that 4021x + 2014y= 1.

A:

Q: 17. Let P1.Pn be positive real numbers such that P1+ + Pn=1. (a) Prove the following: @P² ≥ (ii)…

A:

Q: 4. #x²+x-620, then xs-3 orx 22.

A:

Q: Prove that if x is a real number such that x ≥ 0 and x ≤ € for all € E R where € > 0, then x = = 0.

A: This question is from real analysis.Answer given below.

Q: 4. For each positive integer i, let A, = {x € R| -<x < } = (-;;4) a. Find U-, A;. i=1 b. Find N 4:-…

A:

Q: (c) (For this question, assume that a function f and a number b are given). For every > 0 there…

A: i)  The symbol logic for this statement is  ii) Now the negation of the statement without the…

Q: 4. Show that if x, y, z are integers such that x2 + y2 + z? = 2xyz, then x = y = z = 0. (H)

A:

Q: a. The remainder of P(x) = 2x' +mx? –7 when it is divided by x+2 is 6 greater than when it is…

A:

Q: 43. Show that there cannot exist rational numbers a, b such that V3 = a+b/2.

A:

Q: k* for some constant k". Lp.) Show that L(po)

A: