Porisma

A hint to get started

Compare a cubic approximation with the actual function

Let f(x)=exsin⁡xf(x)=e^x\sin x.

(i) Sketch ff for −3≤x≤3-3\le x\le3. marks

(ii) Expand ff through x3x^3 and call that polynomial g(x)g(x). marks

(iii) On the same diagram sketch and clearly label gg. mark

(iv) For −3≤x≤3-3\le x\le3, find where g(x)g(x) is within ±0.5\pm0.5 of f(x)f(x). marks

[2008/II/1]

CJC · Review problems · Question 10

The polynomial keeps increasing; the actual function has a positive maximum inside the domain.

Read the worked solution