Let x € Z. Prove that if 2 | (x²-5) then 4 | (x²-5).

Q: Find the solution to this recursive relation an = an-1+3, a0=1

A: To Find the solution to this recursive relation an = an-1+3, a0=1

Q: 5. Find the V.A. and H.A. of the function 6-9x Sex a). f(x) : b). f (x) : 2x+5 2ex-1

A: Vertical asymptotes: The line x=L is a vertical asymptote of the functionf(x), if the limit of the…

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: Prove that 2 1 1 5 2 (4-2x)² for all relevant x-values

A: Given is a expression  1215-x>24-2x2. It is required to prove the given expression for all…

Q: Let f(x) = Ax² + Bx + C where A, B and C are real numbers. Prove that if f(x) is an integer whenever…

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Q: Z

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

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Q: Prove that the following is one- to one and onto:  f(x) =x3+2

A: To verify that the given function is one -one onto from R to R (R= the set of real numbers)

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: 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: Prove that if |x-1| < 1, then x² - 2x + 5| < 8.

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Q: prove for every positive real number x that 1+1/x2>=1/x+1/x3.

A: To prove: 1+1x2≥1x+1x3; for everypositive real number x.