<ol class="i-list"><li><div class="list-item-paragraph">Express $\frac{7{{x}^{3}}+{{x}^{2}}+5x+3}{\left( {{x}^{2}}+3 \right)\left( {{x}^{2}}-1 \right)}$ in partial fractions.</div></li><li><div class="list-item-paragraph">Show that when $x&lt;-\sqrt{3}$, $\frac{\mathrm{d}}{\mathrm{d}x}\left( \frac{7{{x}^{3}}+{{x}^{2}}+5x+3}{\left( {{x}^{2}}+3 \right)\left( {{x}^{2}}-1 \right)} \right)&lt;0$.</div></li></ol>

Express $\frac{7{{x}^{3}}+{{x}^{2}}+5x+3}{\left( {{x}^{2}}+3 \right)\left( {{x}^{2}}-1 \right)}$ in partial fractions.

Show that when $x<-\sqrt{3}$, $\frac{\mathrm{d}}{\mathrm{d}x}\left( \frac{7{{x}^{3}}+{{x}^{2}}+5x+3}{\left( {{x}^{2}}+3 \right)\left( {{x}^{2}}-1 \right)} \right)<0$.

Techniques of Differentiation

Question 2c442f10