Question #dc253

1 Answer
Sep 17, 2014

By eliminating common factors, we can find
#lim_{a to 0}{(a-3)^2-9}/a=-6#.

Let us look at some details.

First, we notice that both the numerator and the denominator approach #0# as #a# approaches #0#, which indicates that they share a common factor #a#.

#lim_{a to 0}{(a-3)^2-9}/a#

by multiplying out the square,

#=lim_{a to 0}{a^2-6a+9-9}/a#

by cancelling out the 9's,

#=lim_{a to 0}{a^2-6a}/a#

by factoring out #a#,

#=lim_{a to 0}{a(a-6)}/a#

by cancelling #a#'s,

#=lim_{a to 0}(a-6)#

by plugging in #a=0#,

#=0-6=-6#