Purchase Solution

Epsilon-delta method of limits

Not what you're looking for?

Ask Custom Question

Use the formal definition of the limit (epsilon-delta method) to show that:

(See attached file for equation)

Please be very thorough in your explanation of the solution by showing each step in detail. I really want to understand the method and be able to apply it to other problems. Thanks in advance!

---
(See attached file for full problem description)

Attachments
Purchase this Solution
Solution Summary

This shows how to use epsilon-delta method to verify a limit.

Solution Preview

see attachment

Use the formal definition of the limit (epsilon-delta method) to show that:

Please be very thorough in your explanation of the solution by showing each step in detail. I really want to understand the ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Limits of Functions

    8951 Evaluating Limits: Epsilon-Delta Definition and Limit Theorems Evaluate the following limits using the epsilon - delta definition and the limit theorems.

  • Epsilon-delta definition of limit.

    Given any , there exists (here we choose so that whenever , then So, A limit is found.The Epsilon-delta definitions of the limits are determined.

  • Complex Variables : Use definition of limit to prove things

    The definition of a limit is employed in a proof involving limits, epsilon and delta.

  • Epsilon-delta limits

    | r - 0 | = |r| = (x^2 + y^2 + z^2)^(1/2) This shows how to find limits using epsilon-delta.

  • Integrate 1/(1 + x^a) from zero to infinity

    The limit of delta to zero of the parts parallel to the real axis are: 1) From epsilon + i delta to R + i delta: This becomes in the above limits, the integral from zero to infinity of x^p/(1+x) dx.

  • Limits

    For a function f: A--->R, a real number L is said to be a limit of f at c if, given any epsilon>0 there exists a delta>0 such that if x is an element of A and 0delta then abs(f(x)-L)< epsilon) or the sequential criterion for limits(which states

  • Functions: Limits

    The existence of limits for functions is determined.

  • Limits of Functions

    8950 Limits of Functions Using Epsilon Evaluate the following limits using the epsilon - delta definition and the limit theorems: a) lim {x -> 0} (x^2 + cos x)/(2 - tan x) b) lim {x -> sqrt(pi)} ((pi - x^2)^(1/3))/(x + pi) a.)

  • Functions, Limits & Continuity

    Then give a value for delta > 0 such that for all x satisfying o<|x-x sub 0|<delta the inequality |f(x)-L|< Epsilon holds.

View More Related Solutions