# Homework Help: Taylor polynom and some functionproblem.

1. Apr 13, 2012

### NorwegianStud

Anyone bored enough to wanna help me out with some calculus? I gotta deliver this in 6 hours and can't work these out. Help would be SO much appreciated, I've been at it all night and can't make it out.

1. y^2 - e^sin(x) + xy = sin (x)* cos (y) +3
assume y= y(x) and find y ' (0)

2. Find Taylor polynom of 3rd degree(correct English word?) for x ln x IF x = 1 AND use this to approximate 2 Ln 2. Use the estimate in E3 to find an intervall that contains 2 Ln 2.

3. g(x) = Sin (x) / Cos3 (x).
Show that g(x) have an inverse function in the interval x∈ ( -π/2, π/2). What is D(g^-1)? (Looks like a D, can't find the right one)

AND find the (d/dx)g^-1(x) in the point x = 2. (hint: g(π/4 = 2) )

2. Apr 13, 2012

### NorwegianStud

Bump. Please, anyone. I really need this to get my paper approved, and I don't know where else to ask.

REALLY would be appreciated. If you only can be bothered to solve one that is perfectly fine.

3. Apr 13, 2012

### A. Bahat

What have you tried so far?