Hallar a de modo que h sea continua para todo ax²-x, x≤-1 ax - 5, x>-1 h(x) =m Envie sus comput X real.

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

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Q: 2. Let x1x₂ >. (1+x₁) n . xn> 0 ben real num 1 + x₁ + x1x2 + .. + x1xz

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Q: bijection

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Q: 1. Find the Laplace transform of the function f(t) = eat[a cos(Bt) + b sin(3t)].

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Q: 1. [2x 5 Find x such that 2 3-2 1-2-3 -5 4 X

A: Our objective is given below:

Q: Find the values of a such that det (² 3-x 2 3-x 4 1 -1 -1-x = 0.

A: We have to find the value of x such thatWe know that

Q: (4b) Prove that there exists no positive integer x such that 2x < x² < 3x.

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Q: a) Let f₁ and f₂ be functions from R to R such that f₁(x) = x² and f₂(x) = x − x². What are the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: If x and y are real numbers and x>1, prove that there exists a positive integer n such that xn > y

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Q: Find all non-negative integer pairs of (x, y) such that (xy-7)² = x² + y²

A: Find all non-negative integer pairs of (x, y) such that .

Q: Prove that for all positive real a we have 22 +5 20x4 2 4/5. 24 x2 +5

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Q: Let A = {x € R : x < a} and B={x €R: x < b}, where a and b are real numbers. Show that sup(A+ B) =…

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Q: frx) = Ty-x the domain of suppose What is

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Q: 5x+h over 5x+h+3 minus 5x over 5x+3, all over h. This is a difference quotient problem in…

A: LCD of the numerator is (5x+5h+3)(5x+3).We make both denominators same then subtract the rational…

Q: ve that if x5 – 3x4 + 2x

A: Introduction: In an equation, the two expressions are assumed to be equal, as indicated by the…

Q: Prove there is no real number a such that 28 + x6 + 1 = 2x³

A: The given equation .The aim is to prove the equation has no real solutions.

Q: 2 For 1 X+ 1 and g(x)=, find b. the domain of fo g a. (fo g)(x): a. (fo g)(x)= (Simplify your…

A: Answer: (fog)(x)=2/(x+2)

Q: Let r and s be nonnegative real numbers, f(r) = r" and g(r) = r. %3D Find all pairs r and s such…

A: Given that: f(x)=xr           and             g(x)=xs

Q: 2. Find the Laplace transform of the function g(t) = (1+t+t + t³ + + tm-1 +tm)et.

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Q: Find a pair of values (x, y) that serve as a counter-example for the statement that [ry] : |x||y for…

A: The ceiling function gives smallest integer that is greater than the number, that is, x is the…

Q: Show that if x,y,z,w are real numbers such that x < y and z ≤w, then x + z < y + w.

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Q: a. 2 |x – 4|| х-1 b. x? + 2х — 12 1 х+1

A: a.  (1, 2] and [3, (5+√17)/2]         b.  (-1-√13 , -1+√13)

Q: For an integer t, prove that gcd(2t + 1, 9t + 4) = 1.

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