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Show the following. (a) In(x) << x, (b) 2.3 << el (c) el <<<" (Hint: (9)".
[9] Given any two real numbers x and y such that x < y, show that there exists a rational number q such that x < a <y.
sin (x - 1) x-TT x <T Given f(x) = x2 · Tex + 1, x > Determine if the graph is continuous at it (Show all work)
Q2: Find the complex Fourier series (show your steps) - T < x <07 f(x) 0 < x < Q1: Find the Fourier transform for (show your steps) - 1<x< 0 Otherwise (хе f(x) = { 0,
9. [7 points) Consider the function f(x) defined by f(x) = xeAs + B if x <3 C(x - 3)2 if 3 < x < 5 130 if > 5. C Suppose f(x) satisfies all of the following: f(x) is continuous at x = 3. • lim f(x) = 2 + lim f(x). 3+5+ 3-5- lim f(x) = -4. Find the values of A, B, and C. . 24-O
3. Show the following statements. (a) The set A = {(x, y) € RÝR : x2 + y2 < 1} is uncountable.
. c) + < 2 b) 2 + 3x 27, 0. Solve for r: r' + 2.r < 2.1? +12
1. f(x) c (2xA2xA3sin(x)) and -1<x<1 a. find c b. find E(x) 2. I define El-log(p(x) as entropy. Based on this formula, explain if the entropy of a broken glass is higher or an unbroken glass. 3. f(x) c(3x2 1) and -1<x<1 a. find c b. find E(x) c. find Var(x)
el 37-40 Quadrant in which an Angle Lies Find the quadrant in which 0 lies from the information given. 37. sin 0 <0 and cos e o ( 38. tan <0 and sine < 0
3. Let X and Y have a bivariate normal distribution with parameters x -3 , μΥ 10, σ 25, 9, and ρ 3/5. Compute (c) P(7<Y < 16). (d) P(7 < Y < 161X = 2).
a) b) c) d) The interval notation (-3, 1) described in set builder notation is {* | -3 5xs1} {x-3<x<1) {x-35x<1} {x|-3<x51} The set-builder notation {xl-55x<8} is equivalent to (-5,8) O(-5, 8] O [-5,8) O [-5, 8] To solve 2x - 11<3, one must consider only one case two different cases three different cases O four different cases If f(x) = 3x2 and g(x) = x + 2, then (gf)(x) is 3x2 + 2 3x3 + 6x2 03x2 + x...