Question

The value of $\underset{x\to 0}{lim}\underset{n\to \infty }{lim}({\sec }^{n}x{)}^{{\cos }^{n}x}$ is equal to

• A. 1
• B. 1.00
• C. 1.0

Answer 1

Answer: (A), (B), (C)

$\underset{x\to 0}{lim}\underset{n\to \infty }{lim}({\sec }^{n}x{)}^{{\cos }^{n}x}$
$=e^{\underset{x\to 0}{lim}\underset{n\to \infty }{lim}\frac{\log \left({\sec }^{n}x\right)}{{\sec }^{n}x}}=e^0=1$