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Bernoulli Inequality

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n
2
right edge of window
1
The Bernoulli Inequality states that for
x>-1
and n an integer greater than 1:
n
(1+x)
≥1+nx
with equality if and only if
x=0
. This Demonstration shows, for various integer values of n greater than 1, the graph of the left-hand side of the inequality in blue and the graph of the right-hand side in red. Use the sliders to adjust the value of n and the viewing window and notice that the blue curve is always above the red one, with the only contact occurring at
x=0
.
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