theorem

  1. J

    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. M

    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. F

    Complex analysis- residue theorem

    Is it possible to solve the above using residue theorem? if yes then how to start?
  4. R

    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. F

    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. R

    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. C

    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. U

    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. M

    Proof of fermat's last theorem and beal's conjecture

    What do you think about the attached?
  10. M

    Proof of fermat's last theorem and beal's conjecture

    See attached.
  11. G

    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...
  12. S

    Gauss and Stokes Theorem Problem!! URGENT HELP PLEASE!!

    In $(x, y, z)$ space is considered the vector field $V(x,y,z)=(y^2 z, yx^2, ye^y)$ solid spatial region $Ω$ is given by the parameterization: $\left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =r(u,v,w)=\left[ \begin{matrix} wu \\ wv \\ 2-2w \end{matrix} \right]$ Where $u\in...
  13. C

    Rational Root Theorem

    Hi I am confused on how to use the rational root theorem to help factorise the following problem: 2x^3-7x^2+16x-15 If you could explain how to use this theorem to factorise that would be helpful :) Thanks!
  14. S

    Fundamental Theorem of Line Integrals

    This is another problem from one of my sample tests about line integrals: I know how to get F(x,y), but I have no idea what dr is supposed to be, and how I use y=x^2-1 to determine C.
  15. I

    Fundamental theorem to find definite integrals

    I'm flummoxed by these two problems. The back of the book gives the answers but I'd like to know how to do them. After reviewing my notes, I can't find anything on it. Any help is appreciated 1. Use the fundamental theorem to determine the value of b if the area under the graph of f(x) = x2...
  16. A

    Central Limit theorem

    Dear everyone Greeting, I need help with the question below, to use central limit theorem to prove that the population need not be randomly distributed: John wants to investigate the actual weight of carbonated soft drinks sold in the mart contained in 1.5-litre bottles purchased from a...
  17. A

    Central limit theorem

    Dear everyone Greeting, I need help with the question below, to use central limit theorem to prove that the population need not be randomly distributed: John wants to investigate the actual weight of carbonated soft drinks sold in the mart contained in 1.5-litre bottles purchased from a...
  18. C

    Squeeze Theorem

    Need help using the squeeze theorem with a couple of trig function limits or actually the steps to determine the squeezing functions which I suspect are |x| and -|x| First is \lim_{x\to 0}x \sin{\left (\frac{1}{x}\right )} My take on this one was to start with -1 \leq \sin{\left...
  19. H

    Cauchy-Goursat Theorem Application problem

    Hello Everyone, I am having difficulties with these integrals. I have attempted and I believe my answers are correct, or at least very close, but I have 2 questions: What is the significance of the $C$ being counterclockwise? Would the results be any different if it was clockwise? Am I...
  20. A

    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?