Gods Gift To Calculators: The Taylor Series
Gods Gift to Calculators: The Taylor Series
It is incredible how far calculators have come since my parents were in
college, which was when the square root key came out. Calculators since then
have evolved into machines that can take natural logarithms, sines, cosines,
arcsines, and so on. The funny thing is that calculators have not gotten any
"smarter" since then. In fact, calculators are still basically limited to the
four basic operations: addition, subtraction, multiplication, and division! So
what is it that allows calculators to evaluate logs, trigonometric functions,
and exponents? This ability is due in large part to the Taylor series, which
has allowed mathematicians (and calculators) to approximate functions,such as
those given above, with polynomials. These polynomials, called Taylor
Polynomials, are easy for a calculator manipulate because the calculator uses
only the four basic arithmetic operators.
So how do mathematicians take a function and turn it into......
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