Prove that if |r|< 1, ај Σαr-i i=1

Q: express the set of numbers x satisfying the given condition as an interval.       I x+ 7 I &lt; 2

A: Given: x+7&lt;2 We know that solution of inequalityx+a&lt;b is given by -b&lt;x+a&lt;b

Q: Find the values of m and b that make f(x) differentiable everywhere. f(x) =    x2 if x ≤ 7 mx + b…

A: Given: f(x)=x2x≤7mx+bx&gt;7&amp; f(x) is differentiable. To determine: Value of m &amp; b

Q: Use interval notation to represent all values of x satisfying the given conditions: y = 1 - (x + 3)…

A:

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: Suppose R and S are relations from A to B. Must the following statements be true? Justify your…

A: Here I used counter example to show that the statement one is false and give the proof for statement…

Q: Consider the statement Vxy (y <x) Let x be all natural numbers Let y = x-1 Is the statement true or…

A: We know that the set of natural numbers starts from 1 and it is an infinite set. This set is…

Q: Prove that the second equality is true and find the values of C and δ depending on A, B, ω*.

A:

Q: Let the domain of x be the set of real numbers. Then Vx, (–+1 € R) is O a true statement O a false…

A: Let the domain of x be the set of real numbers.

Q: (a) Prove that if A and B are open, then A+ B is open.

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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: Determine whether each of these statements is true or false. Explain why. 0 ∈ ∅ ∅ ∈ {0} {0} ⊂ ∅ ∅ ⊂…

A: 1.   0 ∈ ∅ As ∅ is empty set so it can't contain any element. Hence 0 can belongs to ∅. Answer:…

Q: 5. Determine whether the set of formulas T = {(Pi + -P;) :i < j, i,j€ N} is satisfiable (pi, i e N,…

A: Answer is mentioned below

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

A: Given

Q: ind the absolute value of z if z= 2 - 11i

A:

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: Q3/ By using definition, proof that cot x = - csc² x. xp

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: Ifx and y are positive real numbers, use the direct method to prove the following inequality: Vxy s*…

A:

Q: 4. Which statement could be proved false using a counterexample? All acute angles are less than 90…

A: We know  the following. Definition:-An acute angle is an angle that measures less than 90 degrees

Q: express the set of numbers x satisfying the given condition as an interval.          I 4x - 1 I ≤ 8

A: 4x-1≤8

Q: Determine all values of x so that det(A) = 0, where

A: Determine all values of x so that det(A) = 0.

Q: Show that the equality [r + y] = [2] + [y] is not valid for all real numbers r and y.

A: Consider the provided question, We first define ceiling function. The ceiling function maps x to the…

Q: o Yes, zero is contained in the interval.

A:

Q: Which of the following expressions is equivalent to for all positive real numbers x and y ?

A:

Q: What are all the possible r values (assuming z is a real mumber) satisfying 24 15 =96? 1=0

A: We will find out the required value of 'x'

Q: Use interval notation to represent all values of x satisfying the given conditions: y = 2x - 11 +…

A: It is given that,y = 2x - 11 + 3(x + 2) and y is at most 0. We have to use interval notation to…

Q: Let x and y be real numbers. Disprove: If |x| < |y| then |x+1|< |y+1]. Let x, y, and z be real…

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: The domain of the function fod- tanh(17-) is (A, 198), Then The value of k- The value of A=

A: Let us consider the given function f(x)=tanh-1x The domain of the function is  x∈(-1,1) The range of…

Q: Suppose x is a real number. Prove that if x 2, then there is a real number y such that x = (2y + 1)/…

A: Domain of a Function The domain of a function explains what values the independent variable, X, can…

Q: Define Floor: R → Z by the formula Floor(x) = for all real numbers x. Here are some example values:…

A: See the proof and counter example below.

Q: Which of the given sentences about stating hypotheses is true? H. can contain the equality. Both Ha…

A: In the given problem we have to answer the sentence about stating hypothesis is true.

Q: I would like a proof to this statement. “Suppose r divides s and s divides t. Then r divides t.”

A:

Q: On what interval(s) is ƒ">0? Give a reason for your answer.

A: Given,  The graph of f'  , the first derivative of a differentiable function f.  Using the graph, we…

Q: The interval notation for the set (xlx ≤4 or x>-2} is. [-2,4] A O (-2,4] BO R .CO DO [-2,4) EO…

A:

Q: Determine whether the following statement is true or false. Justify your answer. If z2, then ee !!

A:

Q: Hi I have attached the question. Thanks

A: To prove that the complex number z is real under the given conditions

Q: What is the statement 0<x< 5 in interval notation? O [0,5] O (0,5) O [0,5) O (0,5]

A: Given 0≤x≤5

Q: 4- find the absolute max.and min. o f the function f = x² +y? Plate boun ded by = x +y? on the…

A:

Q: Which theorem will support the conclusion

A:

Q: The Intermediate Value Theorem can be used to prove that the equation x2 – x – 6 = 0 has at least…

A:

Q: 2 if f) = k x?,-1<x<1,then k = true false

A:

Q: A symbol exists for "parallel" as well as for "perpendicular." O True O False

A: The symbol of parallel is ∥ and perpendicular is ⊥.

Q: Prove the implication: For all real numbers x and y if x + 2y > 42, then x> 21 or y > 10.5.

A: The solution are next step

Q: A 4. Which statement could be proved false using a counterexample? All acute angles are less than 90…

A: The angle which is less than 90 degree is called acute angle

Q: Use interval notation to represent all values of x satisfying the given condition. y = 2x - 11 + 3(x…

A: Use interval notation to represent all values of x satisfying the given condition. y = 2x - 11 + 3(x…

Q: 32 (c) Show that Hence, find the interval for x that satisfies the inequality = 22* 2 x 4" 32" -…

A:

Q: Prove that the statements are FALSE by giving counterexample each.  The sum of two odd counting…

A:

Q: Let z and y be real numbers. Prove that, if 5æ + y > 11, then z> 2 or y > 1.

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.