Answer to Question #87157 in Calculus for johnson

Question

Evaluate the limit limh→0
2(−3+h)2−18
h

limh→02(−3+h)2−18h

Answer 1

$\lim\limits_{h\to 0}(2(-3+h)^2-18h)= \lim\limits_{h\to 0}(2(9-6h+h^2)-18h)=$

$=\lim\limits_{h\to 0}(18-12h+2h^2-18h) =\lim\limits_{h\to 0}(18-30h+2h^2)=$ $\{30h \to 0 \quad as\quad h\to 0 \quad and \quad 2h^2\to 0 \quad as\quad h\to 0,\quad \\hence \quad(18-30h+2h^2)\to 18\quad as\quad h\to 0\}=$

=18.