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## Homework Statement

This question asks you to evaluate the limit of the following function

lim sqrt(9x^2-3x) -3x

x-> infinity

I did it using 2 methods:

1)

lim sqrt(9x^2-3x) -3x

x-> infinity

= lim x(sqrt(9-3/x)) -3x

x-> infinity

= lim 3x - 3x

x -> infinity

= 0

Second Method:

I multiplied by the conjugate radical/conjugate radical and after simplification, I get

lim -3x/6x

x -> infinity

= 1/2

Why is it that I'm getting different answers? Which solution is the right one? Also, how do I type up mathematical formulas? Can someone point me to a LaTex tutorial? Thanks!