# Can one generalize and say that $\lim_{x \to a} k^{f(x)} = k^{\lim_{x \to a} f(x)}$

Can one generalize and say that $$\lim_{x \to a} k^{f(x)} = k^{\lim_{x \to a} f(x)}$$

Is there such a property? Can't find in Calculus books, even though I use that In order to calculate limits with the indeterminate forms $$1^{\infty}$$, $$\infty^0$$ and $$0^0$$.

• If $k$ is a constant, this is simply the definition of continuity. – Ninad Munshi Jul 22 at 2:38

If all limits exist, and $$f$$ is continuous at $$\lim_{x \rightarrow a} g(x)$$, then $$\lim_{x \rightarrow a} f(g(x)) = f(\lim_{x \rightarrow a} g(x))$$.
Apply this theorem to $$f(x) = k^x$$.