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Bernoulli Inequality

Table of Contents:

**(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*:

(1 + x)

(1+5)

6

**Therefore the Bernoulli’s Inequality is 36 > 11**

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