# Functions : Convergence and Limits

Not what you're looking for?

Please see the attached file for the fully formatted problems.

Let f be a real function defined by .

1) Evaluate f'(x), f''(x), f(0). Show that f has exactly two roots and , with . Find an interval of two consecutive real numbers within which the roots must lie.

From now on, let us denote and these two (closed) intervals.

2) Let be the sequence defined by and

a) Show that for all whole natural numbers .

b) Show that if the sequence is convergent, its limit is .

c) Evaluate g'(x). Show that the sequence is convergent and give a sufficient number of iterations N such that the approximation error is no more than .

3) Let and let be the sequence defined by Newton's method starting with . Show that this sequence is convergent. Give its limit. Evaluate .

##### Purchase this Solution

##### Solution Summary

Problems pertaining to limits and functions are solved. The two roots for real numbers are evaluated.

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Solving quadratic inequalities

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

##### Probability Quiz

Some questions on probability

##### Graphs and Functions

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

##### 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.