How do you evaluate the function $f (x) = e^{x}$ $f(x)=e^x$ at the value of $x = 3.2$ $x=3.2$ ?

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How do you evaluate the function $f (x) = e^{x}$ $f(x)=e^x$ at the value of $x = 3.2$ $x=3.2$ ?

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Answer 1 · 2017-07-28T09:44:33

$f (3.2) \approx 24.53253$ $f(3.2) approx 24.53253$

Explanation:

$f (x) = e^{x}$ $f(x) = e^x$

$e^{x}$ $e^x$ is a transcendental function meaning that is both irrational and cannot be expressed in terms of a finite sequence of the algebraic operations of addition, multiplication, and root extraction.

Hence, $e^{x}$ $e^x$ can never (except in the trivial case $x = 0$ $x=0$ ) be expressed as a fraction, the root of any polynomial with rational coeffients or the sum of any finite series. Thus, it can only ever be approximated by a number of any base.

Several definitions of $e^{x}$ $e^x$ exist. Two of the most well known of these are:

$e^x = lim_(n->oo) (1+x/n)^n$ (limit known to exist $forall x in RR$ )

$e^x = sum_(n=0) ^oo (x^n)/(n!)$ (sum known to converge $forall x in RR$ )

From the second definition above we can approximate $e^3.2$ as a decimal as follows:

$e^3.2 = 1 + 3.2 + 3.2^2/(2!)+ 3.2^3/(3!) + 3.2^4/(4!) + .......$

$approx 24.53253$

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How do you evaluate the function $f (x) = e^{x}$ $f(x)=e^x$ at the value of $x = 3.2$ $x=3.2$ ?

1 Answer

Explanation:

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How do you evaluate the function f(x)=e^xf(x)=exf(x)=e^x at the value of x=3.2x=3.2x=3.2?

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How do you evaluate the function $f (x) = e^{x}$ $f(x)=e^x$ at the value of $x = 3.2$ $x=3.2$ ?