How do you find the limit of #3x^3-2x^2+4# as #x->1#?

1 Answer
Steve M
Jan 4, 2017

#lim_(x rarr 1) (3x^3-2x^2+4) = 5 #

Explanation:

If we define #f(x)=3x^3-2x^2+4#, then #f(x)# is continuous everywhere (ie it is well behaved and it has no jumps, discontinuities or places where the function is not defined).

Consequently

#lim_(x rarr a) f(x) = f(a) # for all values of #a#

hence

#lim_(x rarr 1) (3x^3-2x^2+4) = lim_(x rarr 1) f(x) #
# " " = f(1) #
# " " = 3-2+4 #
# " " = 5 #

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