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

Q: Given a real valued function f (x) whi ch is monotonic and differentiable, Prove that for any real…

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Q: lim = 0 || x→00 X X 00

A: To show: limx→∞1x2=0 Solution: Given limit is, limx→∞1x2 As,x→∞,⇒x2→∞And,1x2→0 (As,1∞→0)⇒limx→∞1x2=0

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: Exercise 1. Let f(x) be the function 2х — 1 if x 2. - (a) Find the value of c that makes f(x)…

A: Given f(x)=2x-1if x&lt;-1cxif -1≤x≤2x-2if x&gt;2

Q: Let f(x)= e -x² +1. It can be shown that f has exactly one root, a, on [1, 2]. Find a function g(x)…

A: The following steps are used to find the numerical solution of the equation fx=0 by the fixed point…

Q: x • e e- for x <x < ∞ f(x) elsewhere

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Q: Find the stationary point or points of the function f(x) = ln(x) - (x - 1), and then use this to…

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Q: (2) Let m(E) 1}) = 0. (ii) Show that lim, S f" = m({x € E : f(x) = 1}). E

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Q: x2 – 3x – 2 if x 4 f (x) = - (2x + 1

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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: Let g(x) = kf(x) for all x E/= {x: asxsb}. Show that Jglx)dx = kJ f(x)dx if k<0.

A: To prove the above result we use the definition of lower and upper Riemann integrals. For the proof…

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: The function f(x) = (1+x) O a. Is increasing always O b. Has an absolute maximum at x = - 1 O c.…

A: fx=1+x53 Differentiating with respect to x, we get f'x=531+x53-1=531+x23=531+x132

Q: Show that if n is a natural number and a, ß are real numbers with 8 > 0 then there exists a real…

A: Given that n is a natural number and α,β are real numbers with β&gt;0, then there exists a real…

Q: |x| lim e* +- + x2 X→0-

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Q: ((4— х)2 х 1 continuity at the indicated test point. If it is discontinuous, specify the type of…

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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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