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

Q: What are the global max and min over the interval x E [0, 0) for the graph of f(x) f(x) = (X e)-3x

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Q: Evaluate the function f(x) = e* + In (x + 7) at c, where –7 < c < 6.

A: Given information : f(x)=ex+ln(x+7) 'c' lies between -7 and 6

Q: Define g(-5) in a way that extends g(x) = x² - 25 x + 7x + 10 to be continuous at x = -5.

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Q: Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 2x + 1. 3 h(x) = /2x+1 f(x) =|

A: topic - functions

Q: Show that for all x, e* > 1 +x.

A: It is given that, ex≥1+xwe have to show that for all x.

Q: Show that for all x>0, e* >1+x+÷ 2.

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Q: Find the value of m such that g(x) = {x+5 , if x ≤ m} and g(x) = {2x - 3 , if x > m} is continuous…

A: Function limit and continuity

Q: Let f(x) = ln x and g(x) Show that f(x) and g(x) are both increasing when x > 0. Vr.

A: Given, f(x) = lnx When f(x) is increasing then f'(x) &gt; 0  Differentiating f(x) with respect to x…

Q: Let f(x) = -4x+ 2. Find the largest & so that f(x) - f(a)| < e when |x-a| < 8. S .

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Q: let f(X)=5x +(-3) find the largest & sothat [fx)-F(a]]<E when(x-a/<8

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Q: 2. Let g(x) = [x]. Find: 2.a g ¹({0}) 2.b g¹({-1,0,1}) 2.c g ¹({x 10 < x < 1}).

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Q: The function f(x) = 1/ (x 4 + 6) is continuous for all values of x in R. %3D O False O True

A: We have to determine whether the given function is continous for all values of x in R or not.

Q: Find the value of the constant c that makes the following function continuous on (-∞, ∞). x² { x = 1…

A: The given function is If function continuous at

Q: Evaluate the function f(x) = e* + In (x + 3) at c, where –2.5 < c < 2. (Give your answer as an…

A: Given a function, f(x)=ex+ln(x+3) To find the interval of function at c.

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

Q: Suppose that f(2)=1 and f′(x)≤5 for all values of x. Determine a lower bound for f(−2). Determine an…

A: Given:

Q: Let f(x) = In(x² + 4x + 9) . [Note: f is defined on (–∞,)] (a) (4 points) Find the intervals on…

A: use derivative to find the increasing interval and decreasing interval.

Q: Show that the function f : R → R given by f(x) = x/(1+|x|) is increasing.

A: To find when a function is increasing, you must first take the derivative, then set it equal to 0,…

Q: Prove that if y = f(x) is continuous and f(x) = 0 when x is a rational number, then f(x) = 0 for all…

A: Here, we have been given y = f(x) is continuous and f(x) = 0 when x is a rational number. And we…

Q: lim x→-1 2x + 2 | 1 + x| ||

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Q: Define g(3) in a way that extends g(x) = (x2 - 9)/(x - 3) to be continuous at x = 3.

A: Here, the given function The function gx is continuous at  x=a, if the following holds: (i) ga is…