Question

What is the limit of `(sqrt(3x^4+x^2)` as x approaches 6?

Answer 1

`6sqrt109`

Explanation:

Just plug it in, and you'll get a real answer. If you aren't sure, just plug it in first and check.

`lim_(x->6) sqrt(3x^4 + x^2) = sqrt(3(6^4) + 6^2) = sqrt(3(6^2)(6^2) + (6^2)1)`

`= 6sqrt(3(6^2) + 1) = 6sqrt(3(36) + 1)`

`= color(blue)(6sqrt(109))`

`~~ 6*10.44`

`~~ 62.64`