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Bernoulli Inequality Calculator
Put values in given input box to use our Bernoulli Inequality Calculator.
Table of Contents:
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:
- Bernoulli's Inequality - Proofwiki.org.
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