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

Q: Write the following in interval notation. The set of all real numbers greater than or equal to 4 and…

A: The set of all real numbers greater than or equal to 4 and less than 8

Q: 13. Let U be the set of real numbers, A = {x |x is a solution of x - 1 = 0}, and B ={-1, 4}.…

A: Let's find.

Q: write as interval the set defined on the real line 45 67 8 -3 -2 -1 0 1 2 a) b) -2 c) -5 -4 -3 -2 -1…

A: It is known that, while writing the interval we have to decide that whether the interval is open or…

Q: C and D are sets of real numbers defined as follows. C={z | z>1} D={z |z>8} Write CUD and Cn D using…

A: Given are the sets as follows: C=z|z≥1D=z|z>8. Here z∈ℝ. It is required to find C∪D and C∩D. The…

Q: Let ao, a1,.. .an be real numbers. If ao + ajr+...+a,a" = (x+1) (x+2) ... (x + 672) determine a2+…

A: Suppose we have given a polynomial   then degree of P(x) is sum of degree of all . That is ; .

Q: Determine k so that; is singular.

A:

Q: Let V, = xER for each positive integer i. Find each of the following. (Enter your answers using…

A: As per guidelines, we will solve only first three parts. If want want another part to be solved,…

Q: Let X-bin(7,0.57), then P(X=2) is equal to: O a. 0.1 O b. 0.325 O c. 0.234

A: Binomial distribution allows us to compute the probability of observing specified number of events…

Q: For all real numbers a and b, |a + b| < ]a| + |bl. Select one: OTrue False

A: Answer

Q: For which positive numbers a is it true that ax >= 1+x for all x?

A: Explanation of the solution is given below...

Q: If a = 2a - a² and b =1-(1-a), show that a = b for all natural numbers n. Assume that a, is a fixed…

A:

Q: D and E are sets of real numbers defined as follows. d=z<z4 e=z≥z8 Write  D∪E  and  D∩E  using…

A: D and E are set of REAL numbers.D={z|z&lt;4}D: (-∞, 4)E={z|z≥8}E: [8, ∞)

Q: Find all values of x so that u · u = 50, where

A: Given u·u=x34.

Q: Which one of the following intervals is not symmetric about x= 5? a. (1,10) b. (4,6) с. (3,7) d.…

A: Solution: The objective is to determine which one of the following intervals is not symmetric about…

Q: Let M = R and set Question 2 4= [(-1,5) N*]U ((8,9] (7,10]), B = {æ € R: \r-4|< A= 5x 15-51215} - 4…

A:

Q: 3. Find the distance between (-1, -7) and (5, 9). O V22 O 2v73 O 2v5 O 2V13

A: The distance between the point (x1,y1) and (x2,y2) is given by D=(x2-x1)2+(y2-y1)2

Q: C and D are sets of real numbers defined as follows. C={v|v>4} D-{v| v

A: C ∩ D those element contained in both C and D. C U D those element contained either in C or D

Q: a. Amy will arrive on time while Tess will not b. Both Amy and Tess will not arrive on time.

A: here define events  amy arrive on time  = A Tess arrive on time  = T here arrival of amy and tess on…

Q: 4) if n> 1, then (1+x)" > 1+nx for x E R+ (i.e. x is a non-negative real number). MATH151

A:

Q: Name the preimage of R'. T' T V' R' R Your answer: O T O V O R

A:

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

A:

Q: 19. Which of the following properties of Real Numbers is NOT true ? * a. Vx ER, x+0 = x b. Vx, y, z…

A:

Q: y xy x2 y? 5 2 10 25 15 10 150 100 25 16 400 625 256 35 | 25 Q 1225 625 Σ

A: i solved exactly first 3 subpart because of bartleby policy if you want more please uplode…

Q: Which of the following sets are equal? A = {x e R|-2sxs2} B = {x e Z|-2sx< 2} C= {x e Z*|-2 < xS 2}…

A: So set C and D are equal.

Q: Show that: n n > (xi – x)2 > x? – n(x)2 | i=1 i=1

A:

Q: Which of the following sets are equal?A = { 0 , 1 , 2 } B = { x ∈ R | − 1 ≤ x &lt; 3 } C = { x ∈ R |…

A:

Q: Use Proof by Cases:  If ∀ (x,y) ∈ ℝ^2 (x and y are real numbers), then | |x| - |y| | ≤ |x - y|

A:

Q: C and D  are sets of real numbers defined as follows. C={y|yless than or equal to 4}   D={y|y…

A:

Q: Fix a real number r # 1. For all integers n > 0, 1+r' +r? + •..+ r" = r – 1 pll+1 – 1

A: Consider the provided question,

Q: Let X-bin(18,0.6), then P(5 <= X < 10) is closest to: O a. 0.431 Оь.0.257 O c. 0.435 O d. 0.262 О…

A: If an experiment is performed with possible outcomes as either success or  failure and the…

Q: Which statement is justified by the transitive property of equality? F. (x + y) + z =x+(p +2) G. If…

A:

Q: What is/are X-value(s) in ex2-3x+2)= 1? 1 (2,1) none of these O O

A:

Q: To say that |r – 7| < 2 is the same as saying æ is in the closed interval [A, B] where A is: and…

A: Explanation of the answer is as follows

Q: (-00,2) iss2 in interval notation form. O True O False

A: Solution: x≤2

Q: If x is even and y is odd, show that (x + y)? is odd.

A:

Q: In interval notation, [2, 5) represents the set of real numbers between______ and_______ ,…

A: The given statement is, In interval notation, [2, 5) represents the set of real numbers…

Q: Let B, = {xER|0< x si for each integer i = 1, 2, 3, 4. (a) Find B, U B, U B3 U B4: (Enter your…

A:

Q: B and C are sets of real numbers defined as follows. B = {y|y> 1} C={y|y≤9} Write BUC and B n C…

A: Here, the given sets are: B=y|y&gt;1C={y|y≤9}

Q: Select all that apply Which of the following intervals contains both the integers -1 and 3? (Select…

A: To answer the given question we shall use the following definition of intervals                 a,…

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: If z < o when -0, then 2 is one of the even numbers that is an odd number. O True

A: NOTE- AS  WE ARE ALLOWED TO ANSWER ONE QUESTION IN ONE SESSION SO, I HAVE ANSWERED FIRST QUESTION…

Q: Let X-(1,0,- 1,-/2)'. Then, ||X||∞ =V7 %3D Select one: O True False

A:

Q: If c belongs to the interval (2, 5] but c does not belong to the interval [2, 5), then what is the…

A: Intervals.

Q: Find values of k that satisfy the following equation: JE 1 2 0 1 [1 1 k] 2 3 3 1 k

A:

Q: In interval notation, [2, 5) represents the set of real numbers between and including but not…

A: Given that: In interval notation, [ 2, 5) represents the set of real numbers between  _________ and…

Q: 2. Find all numbers z such that Az3 + Bz² + Cz = D -3 -5 a. A [4] B =[₁₁1] c = L-₁₁ ย -11] A = 11 3…

A:

Q: The three points P(4,3,2); Q(5,4,3) and R(7,6,5) are on the same line. Select one: O True O False

A:

Q: Let s =3t 3-9t -5t+2, find x and v when a=0 O -5 and -14 9 and 14 -9 and 22 -9 and -14 O 5 and 14

A: It depends on how the x and v are defined. By the given function s, we can't say anything about the…

Q: If x is even and y is odd, show that (x + y)² is odd.

A: Let x is even and y is odd. We prove that is (x+y)2 odd.

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.