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 $0^0$.

  • $\begingroup$ If $k$ is a constant, this is simply the definition of continuity. $\endgroup$ – 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 $f(x) = k^x$.


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