f(x)=0 if x≤0, f(x)=x^a if x>0 For what a is f continuous at x = 0...

f(x)=0 if x≤0, f(x)=x^a if x>0

For what a is f continuous at x = 0

For what a is f differentiable at x = 0

For what a is f twice differentiable at x = 0

Expert Solution

Colby Messinger answered 1 year ago

The graph of f(x) = sin(2x)/x is shown in Figure 20. Is the function f(x) continuous at x = 0? Why or why not?

Find f. f ''(x) = x−2, x > 0, f(1) = 0, f(4) = 0 f(x)=

Considering X a continuous random variable defined by the distribution function f(x) = 0 if x<1...

Considering X a continuous random variable defined by the distribution function f(x) = 0 if x<1 -k +k/x if 1<= x < 2 1 if 2<x Find k.

Let X be a continuous random variable with pdf: f(x) = ax^2 − 2ax, 0 ≤...

Let X be a continuous random variable with pdf: f(x) = ax^2 − 2ax, 0 ≤ x ≤ 2 (a) What should a be in order for this to be a legitimate p.d.f? (b) What is the distribution function (c.d.f.) for X? (c) What is Pr(0 ≤ X < 1)? Pr(X > 0.5)? Pr(X > 3)? (d) What is the 90th percentile value of this distribution? (Note: If you do this problem correctly, you will end up with a cubic...

The random variable X has a continuous distribution with density f, where f(x) ={x/2−5i f10≤x≤12 ,0...

The random variable X has a continuous distribution with density f, where f(x) ={x/2−5i f10≤x≤12 ,0 otherwise. (a) Determine the cumulative distribution function of X.(1p) (b) Calculate the mean of X.(1p) (c) Calculate the mode of X(point where density attains its maximum) (d) Calculate the median of X, i.e. a number m such that P(X≤m) = 1/2 (e) Calculate the mean of the random variable Y= 12−X (f) Calculate P(X^2<121)

Consider the function f(x)f(x) whose second derivative is f''(x)=5x+10sin(x)f′′(x)=5x+10sin(x). If f(0)=4f(0)=4 and f'(0)=4f′(0)=4, what is f(5)f(5)?....

Consider the function f(x)f(x) whose second derivative is f''(x)=5x+10sin(x)f′′(x)=5x+10sin(x). If f(0)=4f(0)=4 and f'(0)=4f′(0)=4, what is f(5)f(5)?. show work

A continuous random variable X, has the density function f(x) =((6/5)(x^2)) , 0 ≤ x ≤...

A continuous random variable X, has the density function f(x) =((6/5)(x^2)) , 0 ≤ x ≤ 1; (6/5) (2 − x), 1 ≤ x ≤ 2; 0, elsewhere. (a) Verify f(x) is a valid density function. (b) Find P(X > 3 2 ), P(−1 ≤ X ≤ 1). (c) Compute the cumulative distribution function F(x) of X. (d) Compute E(3X − 1), E(X2 + 1) and σX.

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0...

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0 < x, 0 < y, x + y < 2 and 0 otherwise 1) Find P[X ≥ 1|Y ≤ 1.5] 2) Find P[X ≥ 0.5|Y ≤ 1]

The y-intercept is (0, 0). The x-intercepts are (0, 0), (2, 0). Degree is 3. End behavior: as x → −∞, f(x) → −∞, as x → ∞, f(x) → ∞.

9. Let f be continuous on [a, b]. Prove that F(x) := sup f([x, b]) is...

9. Let f be continuous on [a, b]. Prove that F(x) := sup f([x, b]) is continuous on [a, b]

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