<ol class="i-list"><li><div class="list-item-paragraph">Sketch, on the same axes, the graphs of \(y = -2 + 3^x\) and \(y = \ln(1 - x^3)\), stating clearly the equations of any asymptotes.<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">Hence solve the inequality \(\ln(1 - x^3) \le -2 + 3^x\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Using your result in part <strong>(ii)</strong>, solve the inequality \(\ln(1 + x^3) \le -2 + \frac{1}{3^x}\).<span class="inline-marks">[2]</span></div></li></ol>

Sketch, on the same axes, the graphs of \(y = -2 + 3^x\) and \(y = \ln(1 - x^3)\), stating clearly the equations of any asymptotes.

Hence solve the inequality \(\ln(1 - x^3) \le -2 + 3^x\).

Using your result in part **(ii)**, solve the inequality \(\ln(1 + x^3) \le -2 + \frac{1}{3^x}\).

2024 MI PRU2 P1 Q8

2024 MI PRU2 P1 Q8