David Troyer

2022-01-01

temnimam2

Beginner2022-01-02Added 36 answers

No: If $\in$ is any positive number, then $n}^{\u03f5$ grows faster than $\mathrm{log}n$. This can be clarified in the assertion.

$\underset{n\to \mathrm{\infty}}{lim}\frac{\mathrm{log}n}{{n}^{\u03f5}}=0$

for all $\u03f5>0$. To prove this, just note that by LHospitals rule,

$\underset{n\to \mathrm{\infty}}{lim}\frac{\mathrm{log}n}{{n}^{\u03f5}}=\underset{n\to \mathrm{\infty}}{lim}\frac{\frac{1}{n}}{\u03f5{n}^{\u03f5-1}}=\frac{1}{\u03f5}\underset{n\to \mathrm{\infty}}{lim}\frac{1}{{n}^{\u03f5}}=0$

einfachmoipf

Beginner2022-01-03Added 32 answers

Perhaps T. Bongers has answered the question you meant to ask, but given your mention of the definition of $\mathrm{log}$ I'm not so sure. To answer your question literally, the function $n\to \mathrm{log}\left(n\right)$ is not equal to the function $n\to {n}^{\u03f5}$ for any number $\u03f5$ (not even if $\u03f5$ is "very small.) It is a different kind of function altogether, with very different properties, and it is certainly not defined as a power function.

Vasquez

Expert2022-01-09Added 669 answers

Suppose we seek such

Consider n>1. Then (if

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

Which operation could we perform in order to find the number of milliseconds in a year??

$60\cdot 60\cdot 24\cdot 7\cdot 365$ $1000\cdot 60\cdot 60\cdot 24\cdot 365$ $24\cdot 60\cdot 100\cdot 7\cdot 52$ $1000\cdot 60\cdot 24\cdot 7\cdot 52?$ Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.

A) No

B) 0

C) Yes

D) 6What is a positive integer?

Determine the value of k if the remainder is 3 given $({x}^{3}+k{x}^{2}+x+5)\xf7(x+2)$

Is $41$ a prime number?

What is the square root of $98$?

Is the sum of two prime numbers is always even?

149600000000 is equal to

A)$1.496\times {10}^{11}$

B)$1.496\times {10}^{10}$

C)$1.496\times {10}^{12}$

D)$1.496\times {10}^{8}$Find the value of$\mathrm{log}1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write $\sqrt[5]{{\left(7x\right)}^{4}}$ as an equivalent expression using a fractional exponent.

simplify $\sqrt{125n}$

What is the square root of $\frac{144}{169}$