How to use exponential function?

Question

I know how to use exponential function when required in computer calculator but how does it work? I am still studying and our textbooks are not so detailed which gives us the idea how it works. I am using the function but still anyone can explain me in detail about how does it work?

Let $y = e^x $, after taking value of $x = 1,2,3,4,5,6$. Computer screen displays $e^1, e^2, e^3, e^4, e^5, e^6$. Then what? I don't know how to do it now? Please can anyone explain me? I am good learner can anyone help me?

Main purpose to learn exponential function is I got a question as follows set $A =\{(x,y):y=\exp(x) , x\ \text{belongs to}\ \mathbb{R}\ \text{set}\}$ how to write it in ROSTER form?

Roster form : In this method a set is described by listing elements, seperated by commas, within braces {}. The set of vowels of English Alphabet may be described as {a, e, i, o, u}.

@Mariano Suarez-Alvarez if A = {(x,y): y = e^x , x belongs to R } then write it in roster form. — Murtuza Vadharia, Jun 07 '14 at 08:22
I am sorry, but I have never heard of the term «roster form». In any case, please edit the question to include that information! — Mariano Suárez-Álvarez, Jun 07 '14 at 08:26

score 1 · Answer 1 · answered Jun 07 '14 at 08:42

1

The exponential function can be represented by its Taylor series, $$e^x=\sum_{j=0}^{\infty} \frac {x^j}{j!} = 1+x+\frac {x^2}{2!}+ \cdots $$

answered Jun 07 '14 at 08:42

Mr.Fry

5,003
3
19
28

...which gives sharp approximation only if $x_0=0$, otherwise you need lots of terms, and this destroys the purpose of approximation – Alex Jun 07 '14 at 08:44

score 1 · Accepted Answer · answered Jun 07 '14 at 08:49

1

I do not know which calculator or computer you use neither in which environment. It can be sufficiently clever to display $e^6$ because it noticed that the exponent is an integer. But, tell me what happens if you enter $e^{6.0}$ or $e^{6.00001}$.

For the practical calculation of an exponential, let me be very simple and consider that $$e^x=\sum_{i=0}^\infty \frac{x^i}{i!}$$ If you add $30$ terms (using $x=6$), you should arrive to a value of $403.4287934925$ while the exact value is $403.4287934927$

answered Jun 07 '14 at 08:49

Claude Leibovici

260,315

2

That is certainly not the exact value. – Jack M Jun 07 '14 at 09:11
@JackM. For the number of significant figures I gave, I think it is ! By the way, the $exact$ value does not exist. Cheers. – Claude Leibovici Jun 07 '14 at 09:14
Certainly the exact value exists, it is the irrational number $e^6$. Its decimal expansion starts with the value you gave, but it is not the complete (infinite) expansion, hence not exact. – naslundx Jun 07 '14 at 10:13

How to use exponential function?

2 Answers2