Proof by using intermediate value theorem

Reference no: EM13131941

Let f : [0,1]-->[0,1] be a continuous function. Show that there exists a real number x in [0,1] such that f(x)=x (apply the intermediate value theorem to the function f(x) -x). This point x is known as a fixed point of f, and this result is a basic example of a fixed point theorem.

Reference no: EM13131941

Questions Cloud

Proof of zero test for sequences : Let (a_n) evaluated from n=M to infinity be a sequence of real numbers. Then the limit lim as n-->infinity of a_n exists and is equal to zero if and only if the limit lim as n-->infinity of the absolute value of a_n exists and is equal to zero.

Model for the unemployment rate : Calculate the BIC with the command estat ic and what is the difference between the predicted values and actual for the AR(1), AR(2) and AR(3) models.

What volume (in ml) of this solution would be used : An aqueous solution that contains 329 ppm of KNO3 is being used to feed plants in a graden. What volume (in mL) of this solution is need to prepare 9 L of a solution that is 23 ppm in KNO3?

Find seasonally adjusted sales for second quarter : The same for each of the four quarters next year. The seasonal factor for the second quarter is 145. Determine the seasonally adjusted sales for the second quarter of next year.

Proof by using intermediate value theorem : Let f : [0,1]-->[0,1] be a continuous function. Show that there exists a real number x in [0,1] such that f(x)=x (apply the intermediate value theorem to the function f(x) -x).

Using periodic system cost of goods purchased : Sampson Company's accounting records show the following for the year ending on December 31, 2010. Using the periodic system, the cost of goods purchased is?

Proof lipschitz continuous : Let M>0, and let f:[a,b]-->R be a function which is continuous on [a,b] and differentiable on (a,b), and such that |f'(x)|

How many ml ethanol solution would you need : How many mL of a 22.5% (v/v) ethanol solution would you need to measure out in order to have 12.5 mL of ethanol? The Molar Mass of ethanol is 46.07g/mol.

Proportion of americans drink more than eight servings : Servings of water is approximately normally distributed with a standard deviation of 1.4 serving, what proportion of americans drink a. more than the recommended 8 servings.

User Account

All Pages