Sketch the graphs $y=\text{si}{\text{n}}^{3}x+\text{ln}x$ and $y=1+\text{cos}x$ on the following axes for 0 < $x$ ≤ 9.

Hence solve  in the range 0 < $x$ ≤ 9.

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

       A1A1

Note: Award A1 for each correct curve, showing all local max & mins.

Note: Award A0A0 for the curves drawn in degrees.

[2 marks]

$x$ = 1.35, 4.35, 6.64       (M1)

Note: Award M1 for attempt to find points of intersections between two curves.

0 < $x$ < 1.35      A1

Note: Accept $x$ < 1.35.

4.35 < $x$ < 6.64       A1A1

Note: Award A1 for correct endpoints, A1 for correct inequalities.

Note: Award M1FTA1FTA0FTA0FT for 0 < $x$ < 7.31.

Note: Accept $x$ < 7.31.

[4 marks]