(h) Define f : [0, 2] + R by 122 if 0 <<<1 f(x) = { ifl<152 Using the limit definition of the derivative and the sequence definition of the limit prove that f'(1) does not exist.
A) B) C) 1 Find the Laurent series for 22 +22 for 0 < 121 < 2 Find the Laurent series for (z+2)}(3-2) for 2 – 3) > 5 1 Find the Laurent series for z2(z-i) for 1 < 12 – 11 < V2
find the derivative 6x<+2 ln(x), (1 point) Find the derivative with respect to x of h(x) = h'(x) =
(b) Let X have the pdf x? f(x)= ;-3<x<3, 18 = zero elsewhere. (i) Find the cdf of X
Question 7 (5 points) Let f(x) = 24 and -2x, x < 5 9 3 22, x > 5 Evaluate(gof)(7) A/
(2x - 1 if x < -1 2. Suppose f(x) = 2x2 - 4 if-1<x52 (log: (x - 1) if x > 2 a) Is f continuous at x = -1? Justify your answer completely. b) Is f continuous at x = 22 Justify your answer completely. 3. Suppose f(x) = x2 + 3x a) Using the definition of derivative, find f'(x). No credit will be given if shortcuts are used. b) Find the equation of the tangent line to...
S2 - 2 – 22 if I < 2 Let f(n) = { | 2:- 5 if > 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim, f(a) = 0 Preview lim f(x) = Preview lim, f(z) = 0 Get help: Video Preview Points possible: 1 This is attempt 1 of 2.
How do you do this problem? 3. Let h be a function whose first derivative is h/(x) = S:* 3(In( + 3))? dt. For 6 < x < 12, which of the following is true? Oh is increasing and the graph of his concave down. Oh is increasing and the graph of h is concave up. Oh is decreasing and the graph of h is concave down. 0 h is decreasing and the graph of h is concave up. Oh...
2. A random variable X has a cdf given by F(x) = 1 . x < 0 0 < x < 1 <3 x > 3 11, (f) What is P(X = 1)? (g) Find E(X), the expectation of X. (h) Find the 75th percentile of the distribution. Namely, find the value of 70.75 SO that P(X < 70.75) = F(710.75) = 0.75. (i) Find the conditional probability P(X > X|X > 3).
Example 46. Let X be a random variable with PDF liſa - 1), 1<a < 3; f(a) = { à(5 – a), 3 < x < 5; otherwise. Find the CDF of X. @ Bee Leng Lee 2020 (DO NOT DISTRIBUTE) Continuous Random Var Example 46 (cont'd). Find P(1.5 < X < 2.5) and P(X > 4).