Question

The value that we must assign to $(cosx{)}^{\frac{1}{x}}$ at x = 0 so that the function will be continuous at x = 0 is:

• A. 1
• B. -1
• C. e

Answer 1

The correct option is A 1

$f\left(0\right)=\underset{x\to 0}{lim}(cosx{)}^{\frac{1}{X}}=exp\left(\underset{x\to 0}{lim}\frac{cosx-1}{x}\right)=exp(0)=1$.