(a) Find the limit of the following functions:
-lim as x approaches 0 (1-cos3(x)/x)
-lim as x approaches 0 (sin(x)/2x)
-lim as theta approaches 0 (tan (5theta)/theta)
(b) Find the derivative of the following functions:
-f(x) = cos (3x2-2x)
-f(x) = cos3 (x2/1-x)
(c) Determine the period of the following functions:
-f(x) = 3 cos(x/2)
-f(x)= 21+ 7 sin(2x+3)
Suppose that a random variable X has a pdf
f(x) = ke^(-3x^2+6x-5), -infinity < x < infinity
(a) Find k.
(b) Find the mean and variance of X.
(c) Find the probability that X is between 1 and 1.5.