(Solved):   QUESTION 5 Evaluate the following limits: (a) \( \lim _{x \rightarrow 2}\left(x^{2}+x\righ ...

 

QUESTION 5 Evaluate the following limits: (a) \( \lim _{x \rightarrow 2}\left(x^{2}+x\right)\left(3 x^{3}+6\right) \) (b) \( \lim _{u \rightarrow-2} \sqrt{u^{2}+3 u+6} \) (c) Let \( f(x)=\frac{2 x+12}{|x+6|} \) (i) \( \lim _{x \rightarrow 6^{+}} f(x) \) (ii) \( \lim _{x \rightarrow 6^{-}} f(x) \) (iii) Use (i) and (ii) to deduce lim \( f(x) \) at \( x=6 \). (d) \( f(x)=\left\{\begin{array}{ll}\cos (x) & x<0 \\ 0 & x=0 \\ 1-x^{2} & x>0\end{array}\right. \) (i) Sketch the graph of \( f(x) \). (ii) Is \( f(x) \) continuous at \( x=0 \) ? Give reason(s) for your answer.