Mathematics

Problem

State the value of

\displaystyle \lim_{x\to 0} 5^{x}

and give a brief reason for your answer.

Intuitive explanation

Exponential functions are continuous everywhere, so you can evaluate them by direct substitution—no tricks needed. Since $5^x$ has no discontinuity or undefined behavior at $x = 0$ , just plug in $x = 0$ and use the fact that any positive number raised to the power zero equals one.

Intuitive explanation

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