3. (i) Let A = (a, b) be an arbitrary open interval. Write A as a countable union or a countable intersection of half‐open intervals. (ii) Let B = (a, b] be an arbitrary half‐open interval. Write B as a countable union or a countable intersection of open intervals.

Q: d) do the intervals in the statement of the Nested Interval Theorem need to contain their endpoints…

A:

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

A:

Q: Exercise 33 (i) Let A = (a, b) be an arbitrary open interval. Write A as a countable union or a…

A: Set based ques.

Q: Find the intervals where h(x) = x4 + 24x3 - 168x2 is concave up and concave down.

A: The given functions are,

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

A:

Q: 5- -3.14 3.14 -5- -10- b) Identify the approximate intervals where the graph is concave up.

A: Ans is given below

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: A section of a roller coaster ride is shown. Ax) = 0.001x² – 0.12x² + 3.6x + 10 10 20 30 40 50 60 70…

A:

Q: Describe the set as a union of finite or infinite intervals. {x : |x2 + 2x| &gt; 2}

A: {x:x2+2x&gt;2}

Q: Describe the set as a union of finite or infinite intervals {x : Ix - 4 I &gt; 2}

A: x:x-4&gt;2

Q: A is a subset of the real numbers, R.

A:

Q: which interval of Canvergante is agoce correct of Dower serios { 2-5) conver 6. 6. (0,10

A:

Q: Express the set of numbers x satisfying the given condition as an interval.        I x -4 I &lt; 2

A:

Q: Show that the interval [a,b] is complete

A: Given

Q: Choose the correct intervals of x and y such that (x+y)³ is greater than 8. O A O B x> or y > Oc y>…

A: Y’’ +4y’+ 5y=35 e-4x      y’(0)=1  --&gt; i) Therefore, (D2+ 4D +5)y =0 is homogenous The auxiliary…

Q: Suppose that the possible values of æ is the interval (-3, ). This means that: - x -3 -3 < x < 3

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Explain the difference between the open interval (a, b) and the closed interval [a, b]. Give an…

A: To discuss about open and closed interval

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: 4. Write the upper limits of the class intervals whose class sizes and class marks are given below.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: What is the width of the class interval of 1-3?

A: Width of the class interval

Q: Describe the set S = x :12 x − 3&gt; 4in terms of intervals

A: Given: S=x:12x-3&gt;4 To Describe: Given set in the intervals.

Q: Describe the set as a union of finite or infinite intervals { X : I 2x + 4 I &gt; 3}

A: Given set is x:2x+4&gt;3

Q: Describe the set as a union of finite or infinite intervals. {x : |x − 4| &gt; 2}

A: can be written as x-4&gt;2 or x-4&lt;-2

Q: ne interval of existence for th noo vllangno A

A:

Q: Find the intersection of the given intervals. [1,00) n (-0,5] [1,00) n (- ∞,5] = (Type your answer…

A:

Q: What is the difference between an open interval and a closed interval from a to b?

A:

Q: Use interval notation to represent all values of x satisfying the given condition. y = 8 -  | 5x + 3…

A: The function is y=8-5x+3. The condition is y≥6.   Thus, 8-5x+3≥6.   Simplify. 8-5x+3-8≥6-8…

Q: (b) Using the mean value theorem, prove the inequality, (1+x)“ >1+ ax, where a >1 and x > 0.

A:

Q: Determine the intervals where y = 3x^5 - 15x^4 + 20x^3 - 9 is concave up and concave down.

A: Given the curve y=3x5-15x4+20x3-9 . We need to find the interval in which y is concave up and…

Q: A open interval is homeomorphic to either a closed interval or a half open interval.ture or false?

A:

Q: 1)Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: How do I prove this theorem? Could you include step by step detailed explanation? Theorem: In R,…

A:

Q: Decide whether the following statements are true or false.Provide counterexamples for those that are…

A: Given the statement "The Nested Interval Property remains true if the term “closed interval”…

Q: Determine the vaILus of y Valu that sotisfy the ineauality x*+ x-125. Write youir answer in interval…

A:

Q: Devermine if entinuous or disonfinuous at a given interval. fux) = at (-0,-1)

A: The given function is: fx=4x+1 We have to determine the given function is continuous or…

Q: Describe the set as a union of finite or infinite intervals.  {x : |x 2 -1 | &gt; 2}

A: can be written as x^2-1&gt;2 or x^2-1&lt;-2

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

A:

Q: 1. Write the interval of points that are less than -4: 2. Write the set of points from -5 to 2 but…

A: To find-  Write the interval of points that are less than -4. Write the set of points from -5 to 2…

Q: What is the class mark for a class interval of 19.50—22.50?

A:

Q: Determine the intervals in which solutions are sure to exist. (x² – 9)y + x*y" +2y = 0 Enter the…

A:

Q: Is the number 0.5 above the interval (0.15,0.33)?

A: Given, Interval (0.15,0.33)

Q: Express the set W = {x| -6 < x < 1} using interval notation. Box 1: Enter your answer using interval…

A:

Q: Express the set W = {x|x > 64} using interval notation. Box 1: Enter your answer using interval…

A: W = {x | x2 &gt; 64} In set builder form of set W To express the set W using interval notation

Q: Express the interval using two different representations. -10 -8 -6 -4 o 2 4 8 o 12 -12 10

A: A graph with blank dot at x=6 and move towards right. Concept When we use a blank dot, it means that…

Q: Give 5 examples of phenomena that are expressed as relations of sum, 5 which are expressed by…

A:

Q: If the class boundaries are 16.45 20.55, then the class interval is ......

A: Class intervals is given by 16.50 - 20.50 Then we get class boundary as  (16.50-0.05)  -…

Q: the domain cant be x >3? its a union of intervals?????

A: fx=-3x+1 and gx=x-3

Q: . Find interval of

A: Given power series is: ∑n=1∞3x-2nn+14n Let us consider, un=3x-2nn+14nun+1=3x-2n+1n+24n+1 Then we…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.