Prove that E[X2] < <∞ implies E[[X] <∞. Hint: |X| = |X|I{|X|>1} + |X|I{\X\<1}.

Q: Solve it on the paper! The continuous function g, consisting of two line segments and a parabola,…

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Q: [g(x)f"(x) – Sx)g'(x) g*(x) + C g(x)

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Q: Let g(x) = e² · (x² – 9), g' (x) = e" . (x² + 2x – 9), and g" (x) = e² · (x² + 4x – 7) , Choose one…

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Q: 4. (a) Suppose that a function f satisfies |f (x)| < |x| for all x. Show that f is continuous at 0.…

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Q: 9. Find the value of a so that the function g(x) is continuous at x = 0 where g(x) = { = 1 2xe3x 1…

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Q: Find the value(s) of k such that the function f(x) is continuous on the interval (-∞, ∞). [x2 – 5x +…

A: f(x)={x2−5x+5,x&lt;k2x−7,x≥k

Q: Prove that if f (0) = g(0) and f' (x) ≤ g' (x) for x ≥ 0, then f (x) ≤ g(x) for all x ≥ 0. Hint:…

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Q: 1. Find the monotone interval of y= (x-3)2/4(x-1)

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

Q: Show that for all x E (0, 00) we have In(x) <x – 1. Also, graph the functions In(x) and a - 1…

A: Suppose f is differentiable on an interval where I can be  . Note the result corresponding to…

Q: T « A-Z O F(x) = -2x² - 5x 08-²+2x² OPx)=x² + 2x³ OF(x)=x²-2x Of(x)=2x²³ - 3x +3 0-³²- Ox)=³-2x³²+x…

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Q: 4. Determine the constant m such that f(x) = {x2 + m, if x ≥ 3…

A: Given that: f(x)=x2+m, if x≥32x-m, if x&lt;3