(Solved): 2) Use the difference quotient method to determine the equation of the tangent to the graph of \( ...

2) Use the difference quotient method to determine the equation of the tangent to the graph of \( f(x)=x^{2}-2 x+13 \) where \( x=3 . \quad(A-4 \) marks \( ) \) 3) For the graph of \( y=f(x) \) shown below, determine each of the following limits. \( (A-4 \) marks \( ) \) a) \( \lim _{x \rightarrow 2^{-}} f(x)= \) b) \( \lim _{x \rightarrow 2^{+}} f(x)= \) c) \( \lim _{x \rightarrow 2} f(x)= \) d) \( \lim _{x \rightarrow 0} f(x)= \) 4) As a snowball melts, it's volume decreases. The volume in cubic centimetres is given by the equation \( V(r)=\frac{4}{3} \pi r^{3} \), where \( r \) is the radius in centimetres. Determine, to the nearest tenth, the rate of change of the snowball's volume when its radius is \( 10 \mathrm{~cm} \). ( \( A-4 \mathrm{marks} \) )