Use an example to show that: a)the sum of two even functions is again even b)the product of two odd functions is even c)the product of two even functions is even d)the quotient, when defined, of two odd functions is even.

Q: If x, y and z are three real numbers such that x+ y+ z= 4 and x + y + z = 6, then show that each of…

A: Introduction :

Q: 2. Prove that a) the function f(x) = tan x+x can be replaced by g(x) =x if x→0. b) the function…

A:

Q: Evaluate the sum of with x1 = 0, x2= 2, x3 = 4, x4 = 6, and Ax= 1, for f(x) = 5x -2. i=1 4. i=1

A:

Q: Prove by contradiction that for any positive two real numbers, x and y, if x · y ≤ 50, then either x…

A:

Q: Find the domain of f(x)=x² for 0<x<5. O (1,25] O (0,25) O [0,25] O [1,25)

A: Given: The function is fx=x2 for 0≤x≤5. To find: The domain of the given function. The given options…

Q: The domain of h(x) 7 - consists of all real numbers except 0 and 3, represented in interval notation…

A: Given function is hx=1x+7x-3. To find domain. Solution: Domain of a function is the value of x for…

Q: 5Find The alue of K, to Continue The function f(x) = X-2 4- Ji4+X X #23 %3D - メ=2

A: (5) Given: f(x)=x-24-14+x:x≠2k:x=2 Suppose the function is continuous at x=2. Then,limx→2f(x)=f(2)…

Q: Prove that if a,b belong R(Real Numbers) then |a|-|b| is lesser or equals to |a-b|

A:

Q: Show that if x+yi=(a+bi)- is true, then x-yi=(a-bi)-is all real numbers). true (x, y, a, and b are

A:

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

A:

Q: For each of the functions f1, f2, f3, determine whether it is injective, surjective, and/or…

A:

Q: Prove or disprove that there exist rational numbers x, y EQ such that √11: = x+y√5.

A: Prove or disprove that there exist rational numbers x, y  in Q such that √11 = x+y√5.

Q: The interval ___________ consists of all real numbers for which x ≤ a.

A:

Q: Prove or disprove: If x and y are real numbers with y 2 0 and y(y + 1) < (x + 1)², then y(y – 1) <…

A: We have to prove or disprove that if x and y are real numbers with y≥0 and yy+1≤x+12 ,then yy-1≤x2.…

Q: 1. The set of all pairs of real numbers of the form (x, 0) with the standard operations on R2.

A: 4. Given that the set of all pairs of real numbers of the form (x, 0) with the standard operation on…

Q: Let c, a, ß be nonzero real numbers such that e + B. Find a given that 2n-3 ac 11 c - B'

A: Given, c,α,β be nonzero real numbers such that c≠β, To find the value of α such…

Q: 72. Prove that x 2 − y2 = (x − y)(x + y) for all real numbersx and y.

A: Given equation is x2-y2=x-yx+y

Q: Show that there are an infinite number of rational numbers between any two real numbers x and y with…

A: using Archimedean property to prove above therom...

Q: Can you help me with this?

A:

Q: Show that if fi(x) is O(g1(x)), f2(x) is O(g2(x)), and f2(x) # 0 and g2(x) # 0 for all real numbers…

A:

Q: Let ƒ( θ) = θ3 - 2 θ + 2.Use the Intermediate Value Theorem to show that ƒ has a zero between -2 and…

A: Intermediate Value Theorem: Let f(x) be a polynomial function then intermediate value theorem states…

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: Prove : there exists a real number x such that x^2=3.

A: Let us assume a function f(x)=x2 For x=1, f(1)=12=1  For x=2, f(2)=22=4

Q: Find the supremum and infimum of the set {x € R|10/T – I > 0}, if they exist. If they exist, provide…

A:

Q: Show that if f1(x) isΘ(g1(x)), f2(x) isΘ(g2(x)), and f2(x) ≠ 0 and g2(x) ≠ 0 for all real numbers x…

A:

Q: The function f(x) = 4 for x<2 and f(x) = 4 for x2 2 has domain of all the real numbers. True O False

A: The given function is a constant function. We find it's domain by using the definition of domain of…

Q: Prove that (z - x)(z - y) = (y - x)?. a:= is not a rational number. Hint: Express (x - x) and (z -…

A:

Q: Show that for any real numbers X and y. one of the following two case can happen: Either [x+Y = [×]…

A:

Q: Show that [x+y] ≥ [x]+[y] for all real numbers x and y.

A:

Q: express the set of numbers x satisfying the given condition as an interval.       I 3x + 5 I &lt; 1

A: To solve the inequality: 3x+5&lt;1 Solution: We know that if x&lt;a then -a&lt;x&lt;a. We have…

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

A:

Q: Prove: The difference of the reciprocals of two successive integers equals the product of their…

A: Given, 1n-1n+1    We have to prove the difference of the reciprocals of two successive integers…

Q: 1 The domain of h(x) = - + 7 consists of all real numbers except 0 and 3, represented in interval…

A: Consider a function fx. The domain of a function fx is those values of x for which the given…

Q: Let c, a, ß be nonzero real numbers such that c + B. Find a given that 52n-3 ac2 17 cn–4 n=3 с — в O…

A: According to question given that ∑n=3∞1752n-3cn-4=αc2c-β

Q: Show that : [x+y] > [x] + [Y] for any real numbers x and y

A: Introduction: The greatest integer function is a significant number theoretic function. Every real…

Q: 2) Use Rolle's Theorem on f(x) = 2x3 - 6x² - 2x + 6 to find all numbers c in the interval (1, 3) for…

A: Here is the solution:

Q: For the pairs of integers a=13, b=32, find the gcd g and integers x and y satisfying g=ax+by. Attach…

A: Given that, the pair of integersa=13,b=32 The equation is: g=ax+by where g is the gcd.

Q: Given a function f: R → P(Q), where R is the set of real numbers and P(Q) is the power set of…

A:

Q: a. Use the fact that every nonempty interval of real numbers contains both rational and irrational…

A:

Q: Given an interval [a,b] that satisfies hypothesis of Rolle’s theorem for the functionf(x)=x4+x2−2.It…

A: Rolle's theorem states that "If a function f(x) is continuous on the closed interval [a, b] and…

Q: Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute…

A:

Q: Find all positive rational numbers x and y for which x + and y + - are natural numbers.

A: Natural numbers consists of the set {1,2,3,...}. A positive rational number is in the interval…

Q: Let c, a, ß be nonzero real numbers such that c + B. Find a given that 52n-3 19 cn-4 ac² с — В n=3 O…

A:

Q: Prove or disprove: If x and y are real numbers with y ≥ 0 and                           y( y + 1) ≤…

A: Given equations - yy+1 ≤ x+12             ....................(1)yy-1 ≤ x2…

Q: Prove that the product of an odd function and an even function is odd.

A:

Q: The Intermediate Value Theorem can be used to prove that the equation 2²-2-15-0 has at least one…

A:

Q: Prove or Disprove. for any real numbers x and y, |x+y| = |x| + |y|

A:

Q: Find if the following is homothetic: F (x,y) = x²y +y3 %3D 1. Yes, it is homothetic. 2. No, it is…

A: topic -  homogenous funtion

Q: For f(x) = 4x + 12x, find the number c in (-4, 1) guaranteed by Rolle's Theorem. %3D (Use symbolic…

A:

Q: 1 1 2 x y x+y || +

A: