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Statements

Subject Item
dbr:Binomial_approximation
rdf:type
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Binomial approximation
rdfs:comment
The binomial approximation is useful for approximately calculating powers of sums of 1 and a small number x. It states that It is valid when and where and may be real or complex numbers. The benefit of this approximation is that is converted from an exponent to a multiplicative factor. This can greatly simplify mathematical expressions (as in ) and is a common tool in physics.
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dbt:Reflist dbt:Distinguish dbt:Short_description dbt:Refimprove dbt:Further dbt:Mvar
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dbc:Approximations dbc:Factorial_and_binomial_topics
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n10:Binomial_approximation?oldid=1071764157&ns=0
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dbc:Approximations dbr:Square_root dbr:Big_O_notation dbr:Taylor_series dbr:Smoothness dbr:Calculus dbr:Linear_approximation dbr:Complex_number dbc:Factorial_and_binomial_topics dbr:Bernoulli's_inequality dbr:Taylor's_theorem dbr:Exponentiation dbr:Real_number dbr:Binomial_theorem
dbo:abstract
The binomial approximation is useful for approximately calculating powers of sums of 1 and a small number x. It states that It is valid when and where and may be real or complex numbers. The benefit of this approximation is that is converted from an exponent to a multiplicative factor. This can greatly simplify mathematical expressions (as in ) and is a common tool in physics. The approximation can be proven several ways, and is closely related to the binomial theorem. By Bernoulli's inequality, the left-hand side of the approximation is greater than or equal to the right-hand side whenever and .
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n10:Binomial_approximation