How do you find #\lim _ { x \rightarrow 1^ { - } } \frac { x ^ { 4} - 1} { x - 1}#?
1 Answer
Aug 14, 2017
# lim_(x rarr 1^-) (x^4-1)/(x-1) = 4 #
Explanation:
We seek the limit:
# lim_(x rarr 1^-) (x^4-1)/(x-1) = lim_(x rarr 1^-) ((x^2)^2-1)/(x-1) #
# " " = lim_(x rarr 1^-) ((x^2-1)(x^2+1))/(x-1) #
# " " = lim_(x rarr 1^-) ((x+1)(x-1)(x^2+1))/(x-1) #
# " " = lim_(x rarr 1^-) (x+1)(x^2+1) #
# " " = (1+1)(1+1) #
# " " = 4 #
