Compare a cubic approximation with the actual function

Let $f(x)=e^x\sin x$.

(i) Sketch $f$ for $-3\le x\le3$.2 marks

(ii) Expand $f$ through $x^3$ and call that polynomial $g(x)$.3 marks

(iii) On the same diagram sketch and clearly label $g$.1 mark

(iv) For $-3\le x\le3$, find where $g(x)$ is within $\pm0.5$ of $f(x)$.3 marks