100 fg for each question need it by 11/18 4pm PST
Additionally will need work done and shown through any method via picture uploaded on imgur or whatevers.
Work shown must be detailed and can be legibly read.

will tip extra 200 fg for rules followed. no mistakes please thanks!

http://imgur.com/wrZBgyV

This post was edited by cKranez on Nov 18 2014 03:24am

I don't remember how to deal with questions #3 and #6, but I think I can help in the others.





I hope I could help.

for 3:

tan = sin/cos
cos²(y) + sin²(y) = 1
letting y = arcsin(x), sin²(y) = sin²(arcsin(x)) = x²
cos(arcsin(x)) = sqrt(1-x²)
therefore,
tan(arcsin(x)) = x/cos(arcsin(x)) = x/sqrt(1-x²)

for 6:

for x > 0, |x²sin(1/x)| >= 0
also, for y > 0, |sin(y)| <= 1
letting y = 1/x, |sin(1/x)| <= 1
that is : x²*1 >= |x²sin(1/x)| >= 0 i.e x² >= |x²sin(1/x)| >= 0
lim x² = 0 = lim 0, squeeze rule applies : lim |x²sin(1/x)| = 0 therefore lim x²sin(1/x) = 0

thanks for the replies i will distribute awards accordingly when i get home tonight!