Determine the following limits and draw a rough sketch to illustrate: ( 2 marks each) \( \begin{array}{ll}\text { a) } \lim _{x \rightarrow 3} \frac{x^{2}-9}{x+3} & \text { b) } \lim _{x \rightarrow 3} \frac{x+3}{x^{2}+3 x}\end{array} \)

Calculate the limit \( \lim_{x\rightarrow 3} \frac{x^{2}-9}{x+3} \). Evaluate the limit by following steps: - step0: Evaluate the limit: \(\lim _{x\rightarrow 3}\left(\frac{x^{2}-9}{x+3}\right)\) - step1: Rewrite the expression: \(\frac{\lim _{x\rightarrow 3}\left(x^{2}-9\right)}{\lim _{x\rightarrow 3}\left(x+3\right)}\) - step2: Calculate: \(\frac{0}{\lim _{x\rightarrow 3}\left(x+3\right)}\) - step3: Calculate: \(\frac{0}{6}\) - step4: Calculate: \(0\) Calculate the limit \( \lim_{x\rightarrow 3} \frac{x+3}{x^{2}+3x} \). Evaluate the limit by following steps: - step0: Evaluate the limit: \(\lim _{x\rightarrow 3}\left(\frac{x+3}{x^{2}+3x}\right)\) - step1: Rewrite the expression: \(\frac{\lim _{x\rightarrow 3}\left(x+3\right)}{\lim _{x\rightarrow 3}\left(x^{2}+3x\right)}\) - step2: Calculate: \(\frac{6}{\lim _{x\rightarrow 3}\left(x^{2}+3x\right)}\) - step3: Calculate: \(\frac{6}{18}\) - step4: Calculate: \(\frac{1}{3}\) a) The limit \( \lim _{x \rightarrow 3} \frac{x^{2}-9}{x+3} \) is equal to 0. b) The limit \( \lim _{x \rightarrow 3} \frac{x+3}{x^{2}+3x} \) is equal to \( \frac{1}{3} \) or approximately 0.3. Unfortunately, I am unable to draw a rough sketch at the moment.