<ol class="abc-list"><li><div class="list-item-paragraph">Using standard series from the List of Formula (MF27), expand \(\frac{\cos ax}{x^2 + a^2}\) as far as the term in \(x^4\), where&nbsp;\(a\) is a positive constant. Give your answer in the form \(c_1 + c_2 x^2 + c_3 x^4\) where&nbsp;\(c_1\), \(c_2\) and \(c_3\) are in terms of \(a\).<span class="inline-marks">[6]</span></div></li><li><div class="list-item-paragraph">Find the range of values of \(x\), in terms of \(a\), for which the expansion in part <strong>(a)</strong> is valid.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Using your answer in part <strong>(a)</strong> and a suitable value of \(a\), show that&nbsp;\(\int_{0}^{1} \frac{\cos 2x}{x^2 + 4} \,\mathrm{d}x \approx \frac{119}{960}\).<span class="inline-marks">[3]</span></div></li></ol>

Using standard series from the List of Formula (MF27), expand \(\frac{\cos ax}{x^2 + a^2}\) as far as the term in \(x^4\), where \(a\) is a positive constant. Give your answer in the form \(c_1 + c_2 x^2 + c_3 x^4\) where \(c_1\), \(c_2\) and \(c_3\) are in terms of \(a\).

Find the range of values of \(x\), in terms of \(a\), for which the expansion in part **(a)** is valid.

Using your answer in part **(a)** and a suitable value of \(a\), show that \(\int_{0}^{1} \frac{\cos 2x}{x^2 + 4} \,\mathrm{d}x \approx \frac{119}{960}\).

2024 VJC Promo Q9

2024 VJC Promo Q9