1. Limit prove Derivative

$$ Ex:\ \sqrt {a-x} $$

1. Take Limit (piece, L’H, Simplify)

$$ Ex:\ \lim_{x->0} (\frac {13} x +\frac {13} {|x|}) $$

1. Continuity (Piece wide definition function)

$$ Ex: \ f(x) = \begin{cases} x+5 & x< 0 \\ (x-a)^2 +b & 0\leq x< 2 \\ 1 & x\geq 2 \end{cases}

$$

1. Derivative

$$ Ex :\ x^2y^2 $$

1. Solve tangent line

$$ y^2(y^2-4) = x^2(x^2-5)\ Point:\ (0,-2) $$

1. Relative rate

Square initially gas dim 18cm x 27cm side, a is decreasing at a rate of 2 cm/sec and b is increasing at a rate 3 cm/sec …… after 5 second.