Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

Limit x tends to infinity ((x+1)(x+2)(x+3))^1/3-x=?

1 Answer

Apr 19, 2018

$1$

Explanation:

$(x+1)(x+2)(x+3) = x^3+bx^2+cx+d$

$root(3)((x+1)(x+2)(x+3)) = root(3)(x^3+bx^2+cx+d)$

$= root(3)(x^3(1+b/x+c/x^2+d/x^3))$ $" "$ for $x != 0$

$= xroot(3)(1+b/x+c/x^2+d/x^3))$ $" "$ for $x != 0$

So

$lim_(xrarroo)((x+1)(x+2)(x+3))^(1/3)/x = lim_(xrarroo)root(3)(1+b/x+c/x^2+d/x^3)$

$= root(3)(1+0+0+0) = 1$

Related questions

Impact of this question

10499 views around the world

You can reuse this answer
Creative Commons License