# theorem

1. ### Squeeze Theorem

Our professor want us to prove that lim sin x / x as x goes to 0 = 1 by using Squeeze Theorem. He told us that sin x will be between tan x and x. I did this tan x <= sin x <= x tan x / x <= sin x / x <= x/x sin x / x cos x <= sin x / x <= 1 now I will take the limit (lim sin x / x as x...
2. ### Do I not have enough information to do these problems? (limits with squeeze theorem)

m.imgur.com/x55Btsf <----- Notes I have from lecture on squeeze theorem. I realize range for sin and cos = [-1,1] and tan and cot are all real numbers. he showed us these 2 cases for squeeze theorem, then we went over the review for the exam on Tuesday. While doing the...
3. ### Complex analysis- residue theorem

Is it possible to solve the above using residue theorem? if yes then how to start?
4. ### Justifying an extreme value theorem?

I was looking through the coursework document on college board and one sentence says there are three ways to justify an extreme value. What are these three ways?
5. ### vector calculus- application of Stoke's theorem

Q1. Use Stoke's theorem to evaluate int(x^2*exp(5*z) dx +x*cos y dy+3*y dz) around a closed curve C where C is defined by the parametric equation x=0, y= 2(1+cos t), z=2(1+sin t), 0<=t<=2 Pi. Q2. Let S denote the surface of a cylindrical solid bounded by x^2+y^2 =...
6. ### Calculus questions about IVT and EVT?

I have these questions to do for homework and I am really stuck (Worried) (look at the picture in the link) [COLOR=#000000][FONT=&amp]The only thing I have so far is that 1C is impossible and that 1D is just basically any continuous function. I need help with the other questions - any type of...
7. ### Cauchy's Theorem in complex functions

Hi everyone, I'm starting off with complex numbers and functions and would need a little help from you guys. I have the following equation: Evaluate the closed integral of: e^z/(z*(z^2+4)) where C = {abs(z)=1} clockwise and then C={abs(z)=3} anticlockwise. I was told to first check...
8. ### Steep Diagonals and Magic Squares - Prove and State a Theorem

[/FONT] [/CENTER] [/TD] We want to describe via a picture a set of subsets of a square which are something like diagonals, but are not quite the same. We’ll call them steep diagonals. One of them, labelled e, is illustrated in the square below; the other 6 are parallel to it. State and prove a...
9. ### Proof of fermat's last theorem and beal's conjecture

What do you think about the attached?
10. ### Proof of fermat's last theorem and beal's conjecture

See attached.
11. ### Green's theorem

I need a little help with the problem below: This is my issue with this question: I know the formula for Green's theorem. I worked through the problem and ended up with (-5/3). The answer was 5/3. The order of integration the lecturer used to solve the ensuing double integral was "dydx". I...

20. ### The Central Limit Theorem

The image contains the problems and the solution. In the calculation, 0.027, which is the difference between the mew and the x-bar changed from 0.027 to 2.7. Why do we need to move the decimal two digits to the right?