Suppore x is rational, then there exist a rational number n so that x = 1/₂ 2 L n бо, е (ex) = = e Raise both sides to the power n & what do we get? Recall, the product of n real numbers or x/ 2. So, é I real numbers in n always real. is a real number for any. real even if we have to think of x as the limit of a sequence of of a sequence of rational number x numbers.

Q: Ix-51>7* O x>7, x 12, x 12 No Solotion

A: We have to solve the inequality

Q: -(+2h)+16f (x+h)-30f(x)+165 (x-h)-(-2h) Suppose f"(x) 3 Show that the error is O(h4)

A: It is given that,

Q: If X~N(2,9), compute a. P(X>=2) b. P(1<=X<7) c. P(-2.5<=X<=-1)

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 4 z+9 (z – 2) + 2 (9 – 2) < 18 (x + 1) Enter the exact answer in interval notation. -To enter 00,…

A:

Q: (Z over 8) - (1 over 2) = (z over 6)

A: Given equation is

Q: find lim (-5) h-->0 does not exist O -5 O none of these answers

A:

Q: Identify the open intervals on which the function is decreasing. (Enter your answers using interval…

A: Let f(x)=y. Differentiate the function with respect to x, to find f'(x).…

Q: 5. Which function does NOT have an asymptote of x = 3? * 1 ソ= ズ-3 4. ソ= (x- 3)2 Option 1 Option 2 2x…

A: An asymptote  is a straight line that constantly approaches a given curve but does not meet at any…

Q: For all x, there exists y such that (y^2 <= x <(y+1)^2) when domain is N(natural number) I want to…

A: For all x, there exists a y, such that,  y2 ≤ x &lt; (y + 1)2   Given that x is a natural number,…

Q: State the domain of the rational function. x-9 8) f(x)= x2.5 A) (, -) O--,-3)u(-3,3)u (3, ) B)…

A: To find the domain of the below rational function. fx=x−9x2+5 fx=11x+5

Q: 1) If f (x) = 1 x-7 then f-1 (x) =2x+7                   2                 a) true  b) false…

A:

Q: Monte Carlo integration is a method to numerically estimate integral like I(g) = Sa g(x)dx. The idea…

A: According to the law of large numbers, if X1, X2,…, Xn is a sequence of random variables with mean μ…

Q: Example for unboundedness Min -2₁-3x2 2₁-22₂54 -2₁ + x₂ 5 3 x2 x₁, x₂ > 0 s.t

A:

Q: Which of the following is the contrapositive statement for the statement ″if f(x) ≥3, then x 9,…

A: We are given the statement  ″if f(x) ≥3, then x &lt;9″we need to write contrapositive of this…

Q: If x is any real number, then cosh x Σ n=0 n! + 198 Σ n=0 (-x)" n!

A:

Q: » (6)- (:) + (2) ---» :) - (3) n n +(-1)" (" ). = 0. с) + 3 n +...+n = n2"-1.

A:

Q: If X ~ N(80, 144) then find (90< x<100).

A: GivenX~N(80,144)Mean(μ)=80variance(σ2)=144standard deviation(σ)=144=12

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: -5/7-3x with two intervals 36/5 and 19/5

A: For two Intervals  (36/5, 19/5) For X= 36/5 The Value of given expression is,

Q: Question 7 A = {x: <. *} = v 2x-1 3 {x: - %3D 5 < 3x + 2} B = (10 a) Find ANB b) Illustrate your…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: f(1) = 5 and f(n) = 6 + F(n-1) Fornz2 N

A:

Q: О P/Z 1.5) О PZ < 1.96) О Р85 О Р25

A: Here use normal distribution table for find probability from z score

Q: 11. If two rational functions have the same restrictions, are they equivalent? Explain and…

A: We will check if they are equivalent.

Q: 3/4(8y-9)&lt;3

A: We multiply both sides by 4 first.

Q: • If x = -0,8, then [x-1]%D %3D 1. -2 2. -1 3. -0.8 4. 1

A: Greatest integer function: For all real numbers x, the greatest integer function gives the largest…

Q: n=1 00 x E (Use symbolic notation and fractions where needed. Give your answers as intervals in the…

A: For the given series we have to find the interval of convergence.

Q: Which of the following is an oblique asymptote of 0 يع | من O 3 O 814 x 3 4 - - I + Y = 1 4 13 Y 4…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Which of the following is not an asymptote of * 4x² y = x²-9 Ox=3 O y = -4 Oy=4 O X=-3 ?

A: To find Which of the given is  not an asymptote of y.

Q: Refer to Example 3 to find a value of 8 > 0 such that 1 then 1 If 0 < |x – 3| < 8, < 10-4 3 - - -

A: Consider : 1x-13&lt;10-4 if x-3&lt;δ. Find δ. Since,…

Q: 11 lim e-Siny-1 e- Siny-1 0-1-1 X-70 X4+ Ex+12x 0+0 t0

A:

Q: Give the domain for  g(x)=x+2/x^2−3x−40 in interval notation.

A:

Q: (8x²-8x²e* 5. lim x3 А. 8 В. 1 С. -8 D. 0

A: We will find the limit

Q: Find the critical points and the intervals on which the function f(x) = (x³ – 4x) e* + 15 is…

A: given f(x)=x3-3247xex +15 we have to find the critical points and the intervals on which the given…