EXERCISES

1. (5) If $g(x) = \vert\vert 3x \vert\vert,$ calculate $\nabla g(x).$
2. (10) Suppose $g:\Re^n \rightarrow \Re,~ a,b \in \Re^n,$ and $f(t) := g(a-tb)$. Calculate $f^\prime (t).$

3. Write down the Taylor series of:
   1. (5)
      
      $$f(x) = x^5+x^3, \mbox{~about~} x=1.$$
      
      

   2. (5)
      
      $$f(x) = \log(1+x), \mbox{~about~} x=0.$$