Please explain and show how to find the answers to the following problems: 1. Wh
ID: 1891259 • Letter: P
Question
Please explain and show how to find the answers to the following problems:1. What does the graph of {(sin t, cost t): -pi/2 <= t <= 0} in the xy-plane look like?
2. Integral from 0 to 1 of (x)/(1 + x^2) = ?
3. If S is a nonempty finite set with k elements, then the number of one-to-one functions from S onto S is?
4. Let g be the funtion defined on the set of all real numbers by:
g(x) = {1 if x is rational,
{e^x if x is irrational,
Then what is the set of numbers at which g is continuous?
Sorry I couldn't use the equation editor because it kept freezing my computer several times. I tired my best to type the problems so you can read them easily. If you have questions please ask. Thanks for any help!
Explanation / Answer
2.
Integral from 0 to 1 of (x)/(1 + x^2)dx
= (1/2)[Integral from 0 to 1 of (2x)/(1 + x^2)]dx
=(1/2)[log(1+x^2)](0,1)
=(1/2)[log(1+1) - log(1+0) ]
=(1/2)log2