How do you find limits as x approaches infinity?

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Answer 1 · 2014-11-07T12:14:24

Example 1

#lim_{x to infty}{x-5x^3}/{2x^3-x+7}#

by dividing the numerator and the denominator by #x^3#,

#=lim_{x to infty}{1/x^2-5}/{2-1/x^2+7/x^3}={0-5}/{2-0+0}=-5/2#

Example 2

#lim_{x to -infty}xe^x#

since #-infty cdot 0# is an indeterminate form, by rewriting,

#=lim_{x to -infty}x/e^{-x}#

by l'Hopital's Rule,

#=lim_{x to -infty}1/{-e^{-x}}=1/{-infty}=0#

I hope that this was helpful.