Can anyone explain to me how

$f(n)={n}^{0.999999}\mathrm{log}n=O({n}^{0.999999}{n}^{0.000001})$?

$f(n)={n}^{0.999999}\mathrm{log}n=O({n}^{0.999999}{n}^{0.000001})$?

pliwraih
2022-07-16
Answered

Can anyone explain to me how

$f(n)={n}^{0.999999}\mathrm{log}n=O({n}^{0.999999}{n}^{0.000001})$?

$f(n)={n}^{0.999999}\mathrm{log}n=O({n}^{0.999999}{n}^{0.000001})$?

You can still ask an expert for help

asked 2022-07-17

I know that fraction denominator needs to be > 0 , so if denominator is quadractic equation i know how to solve , But since denominator is > 0 , I dont know how to solve , can anyone help me ?

$f\left(x\right)=\sqrt{\mathrm{log}\left(\frac{3x-{x}^{2}}{2}\right)}$

$f\left(x\right)=\sqrt{\mathrm{log}\left(\frac{3x-{x}^{2}}{2}\right)}$

asked 2022-07-21

Help me with this

$\int \frac{{\mathrm{ln}}^{3}x}{x}\text{}dx$

Is this the same as

$\int \frac{(\mathrm{ln}x{)}^{3}}{x}\text{}dx\phantom{\rule{thickmathspace}{0ex}}\phantom{\rule{thickmathspace}{0ex}}?$

$\int \frac{{\mathrm{ln}}^{3}x}{x}\text{}dx$

Is this the same as

$\int \frac{(\mathrm{ln}x{)}^{3}}{x}\text{}dx\phantom{\rule{thickmathspace}{0ex}}\phantom{\rule{thickmathspace}{0ex}}?$

asked 2022-07-22

I just wonder can we call ${2}^{x}+x$ an exponential function or not?

With the same way of thinking is ${\mathrm{log}}_{2}(x)+x$ a logarithmic?

With the same way of thinking is ${\mathrm{log}}_{2}(x)+x$ a logarithmic?

asked 2022-08-20

I have the following limit:

$\underset{x\to +\mathrm{\infty}}{lim}\frac{\mathrm{log}({e}^{2x+1}+x)}{x}=2$

I know for sure that

$\underset{x\to +\mathrm{\infty}}{lim}\frac{\mathrm{log}x}{x}=0$

Because x grows a lot faster than $\mathrm{log}x$. Then why wouldn't the first limit be equal to 0 as well?

$\underset{x\to +\mathrm{\infty}}{lim}\frac{\mathrm{log}({e}^{2x+1}+x)}{x}=2$

I know for sure that

$\underset{x\to +\mathrm{\infty}}{lim}\frac{\mathrm{log}x}{x}=0$

Because x grows a lot faster than $\mathrm{log}x$. Then why wouldn't the first limit be equal to 0 as well?

asked 2022-08-11

use the laws of logarithms to expand the expression

${\mathrm{log}}_{3}(\frac{x({x}^{2}+5)}{\sqrt{{x}^{2}-5}})$

${\mathrm{log}}_{3}(\frac{x({x}^{2}+5)}{\sqrt{{x}^{2}-5}})$

asked 2022-08-14

Do the logarithmic rules work when taking logs of functions as opposed to numbers?

i.e. suppose f is a function and n is a real number, is $\mathrm{log}(f(x{)}^{n})=n\xb7\mathrm{log}(f(x))$?

i.e. suppose f is a function and n is a real number, is $\mathrm{log}(f(x{)}^{n})=n\xb7\mathrm{log}(f(x))$?

asked 2022-09-23

Given a constant sum of ${x}_{n}$ values:

$\sum _{n=1}^{N}{x}_{n}=C$

where ${x}_{n}\ge 1$

Find the maximum of the following expression:

$\sum _{n=1}^{N}{a}_{n}\mathrm{log}\left({x}_{n}\right)$

where the ${a}_{n}>0$ values are constants, and the ${x}_{n}$ values are free to change, given that their sum will remain constant.

$\sum _{n=1}^{N}{x}_{n}=C$

where ${x}_{n}\ge 1$

Find the maximum of the following expression:

$\sum _{n=1}^{N}{a}_{n}\mathrm{log}\left({x}_{n}\right)$

where the ${a}_{n}>0$ values are constants, and the ${x}_{n}$ values are free to change, given that their sum will remain constant.