How do you find the limit of #x^3-x# as x approaches #0^-#?

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Answer 1 · 2017-08-06T23:29:20

# lim_(x rarr 0^-) x^3-x = 0 #

Let:

# f(x) = x^3-x #

Then #f(x)# is a polynomial of degree three, and is therefore continuous over its entire domain.

So:

# lim_(x rarr 0^-) f(x) = lim_(x rarr 0^+) f(x) = f(0) #

And:

# f(0) = 0#

Hence:

# lim_(x rarr 0^-) x^3-x = 0 #