How do you evaluate #\lim _ { h \rightarrow 0} \frac { a ^ { 2} + 2a h + h ^ { 2} - a ^ { 2} } { h }#?
1 Answer
Aug 14, 2017
# lim_(h rarr 0) (a^2+2ah+h^2-a^2) / h = 2a #
Explanation:
Let use denote the limit by:
# L = lim_(h rarr 0) (a^2+2ah+h^2-a^2) / h #
Then
# L = lim_(h rarr 0) (2ah+h^2) / h #
# \ \ = lim_(h rarr 0) (2a+h) #
# \ \ = 2a #
Hence:
# lim_(h rarr 0) (a^2+2ah+h^2-a^2) / h = 2a #
