• A is open in X. • A = Int A • A contains none of its boundary points. • Every point of A has a neighborhood contained in A.

Q: Let α and β be positive integers and X ~ Geo(p). Show that P(X > α + β | X > α) = P(X > β) = qβ

A: Given: X ~ Geo(p) f(x)=qx-1p x=1,2,3... P(X > α + β | X > α) = P(X > β) = qβ

Q: 2) Let m and n be positive integers. Use the Convolution Theorem to evaluate the integral…

A: Let m and n be positive integers. The objective is to evaluate the integral ∫0t(t-τ)mτndτ by using…

Q: In an integral domain, show that a and b are associates if and only if<a> = <b>.

A:

Q: 2. Find the interior, the boundary, the set of all accumulation points, and the closure of each set.…

A:

Q: 5. Let (a, b] denote an interval of the real axis, containing the boundary Doint b, but not…

A: Answer given below.

Q: 23. Determine whether each of these functions is a bijection from R to R. a) f(x) = 2x + 1 b) f(x) =…

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Q: 5. By the Fundamental Theorem of Calculus (Newton-Leibnitz Theorem) √² + x² d VX evaluate

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Q: 3) √³/₂2 5 - dx -2 2x-1

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Q: 3. Show that is a closed subset of R². {(x, y) = R²: y = x²}

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Q: is x=0 considered a vertcial asympptope?

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Q: f(x + a) dx = f(1) dæ = | f(x) d.r. -T+a

A: Proving of integral of periodic function

Q: Let A and u be positive real numbers. Then Jp(Ax) and Jp(ux) satisfy d d + dx dx (11.6.37) d ( d p²…

A: