scroll-up
X

Bernoulli Inequality Calculator

Put values in given input box to use our inequality calculator.

Table of Contents:

Is This Tool Helpful?

     

Formula

(1 + x)r ≥ 1 + rx

Where,
x ≥ -1 and x ≠ 0,
r ≥ 1.

Bernoulli’s Inequality is defined as an inequality that approximates exponentiations of 1 + x. Here, the inequality states that for every integer r ≥ 0 and every real number x ≥ −1. If the exponent r is even, then the inequality is valid for all real numbers x. The strict version of the inequality is that for every integer r ≥ 2 and every real number x ≥ −1 with x ≠ 0.

This advanced online Bernoulli Inequality Calculator is used to calculate the inequality of any given function by putting the values for x value and power raised to that value.

Example:
Calculate the inequality of number for the given details.
x Value: 5
Power (r): 2

Solution:
Apply Formula:
(1 + x)r ≥ 1 + rx
(1+5)2 ≥ 1+2*5
62 ≥ 1+10
36 > 11

Therefore the Bernoulli’s Inequality is 36 > 11 

References: 

  1. Bernoulli Inequality -- from Wolfram MathWorld.
  2. Bernoulli's Inequality - Proofwiki.org.