Let a > 0 and b>0 be constants. Find the radius of convergence and interval of convergence of the following series. (x - a)" Ln2 + b You must show all of your work and state which tests you are using.
Suppose f is continuous, f(0)=0, f(2)=2, f'(x)>0 and f (x) dx = 1. Find the value of the integral fro f-?(x) dx =?
Find the Laplace Transform
(d) f(t) = te, 0<t<1, et, t > 1. l
8. Let f (x) e, 0 > 0; x> 0 (1 1 +e (a) Show that f(x) is a probability density function (b) Find P(X> x) (c) Find the failure rate function of X
f(x+h)-f(x) a) Find the difference quotient- -> (assume h + 0) for f(x) = x2 + 3x + 4 b) Find the inverse algebraically of g(x) = 2x-3
Exercise 6. Show that if f(x) > 0 for all x e [a, b] and f is integrable, then Sfdx > 0.
4- Find f'(x) if f(x) is the given expressions. i) f (x ) = zsin ">" + ln cosh - 4x ii) f(x) = tanh-- 4x etanh4x
-3x > 0 An exponential distribution is given by f(x) zero, x <0 Find the distribution of the random variable Y X2
Find the area under the graph of g over [-2, 3] g(x) = -x? +5 when x 50 g(x) = x + 5 when x > 0
Q1 Question 1 2 Points Find the inverse of f-1 of the function f(x) =1+1, 2 > 0. of'() = -1 of '(x) = -1 of '(x) = Of-l does not exist