Given #k(x) = (x^3 - 2x - 4)/(x-2)# how do you find the limit as x approaches 2?

1 Answer
Jim H
Jan 23, 2017

Factor, reduce and evaluate.

Explanation:

#lim_(xrarr2) (x^3-2x-4)/(x-2)# has indeterminate initial form #0/0#.

Since #2# is a zero of the polynomial #x^3-2x-4#, we can be certain that #x-2# is a factor.

Use division (long or synthetic) or step-by-step reasoning to find

#x^3-2x-4 = (x-2)(x^2+2x+2)#

#lim_(xrarr2) (x^3-2x-4)/(x-2) = lim_(xrarr2) ((x-2)(x^2+2x+2))/(x-2)#

# = lim_(xrarr2) (x^2+2x+2)#

# = 4+4+2 = 10#

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