Question

Evaluate: $\underset{x\to \frac{\pi }{4}}{lim}\frac{{cot}^{3}x-tanx}{cos(x+\pi /4)}$

• A. $8$
• B. $8\sqrt{2}$
• C. $4$
• D. $4\sqrt{2}$

Answer 1

Answer: (A)

$8$

Using L'Hopital rule:

$\underset{x\to \frac{\pi }{4}}{lim}\frac{{cot}^{3}x-tanx}{cos(x+\pi /4)}=\underset{x\to \pi /4}{lim}\frac{-3{\cot }^{2}xcose{c}^{2}x-{\sec }^{2}x}{-sin(x+\pi /4)}=\frac{-3\times 1\times (\sqrt{2}{)}^2-(\sqrt{2}{)}^2}{-1}=8$