Is this a valid way to solve $\lim_{x \to \infty} \frac{\log({x^2-x+1)}}{\log{(x^{10}+x^5+1)}}$

Asked Dec 17 '19 at 17:28

Active Dec 17 '19 at 17:40

Viewed 64 times

$$\lim_{x \to \infty} \frac{\log({x^2-x+1)}}{\log{(x^{10}+x^5+1)}}=\lim_{x \to \infty} \frac{\log({x^2(1-1/x+1/x^2)}}{\log{(x^{10}(1+1/x^5+1/x^{10})}}=\lim_{x \to \infty} \frac{\log({x^2})\log{(1-1/x+1/x^2)}}{\log{(x^{10})\log{(1+1/x^5+1/x^{10}})}}=\lim_{x \to \infty} \frac{2\log x}{10\log x}=1/5$$

Is it correct?

edited Dec 17 '19 at 17:40

Z Ahmed

43,235

asked Dec 17 '19 at 17:28

Milan

1,631

7

$\log(ab)=\log(a)+\log(b)$ not $\log(a)\cdot\log(b)$ – saulspatz Dec 17 '19 at 17:29
@saulspatz thanks, should i close the question it is so simple after seeing the mistake – Milan Dec 17 '19 at 17:31
If it were me, I'd delete the question – saulspatz Dec 17 '19 at 17:35
3

But please don't delete the question, it is useful for anyone else who wonders the same thing. – MPW Dec 17 '19 at 17:35

Is this a valid way to solve $\lim_{x \to \infty} \frac{\log({x^2-x+1)}}{\log{(x^{10}+x^5+1)}}$

0 Answers0