Mathematics

Problem

Which one of the following limits equals

1

? a)

\displaystyle \lim_{x\to\infty}\Bigl(1+\tfrac{1}{x}\Bigr)^{x}

\displaystyle \lim_{x\to2}4^{\,x-2}

\displaystyle \lim_{x\to1}\log_{3}(x)

\displaystyle \lim_{x\to0^+}\dfrac{5^{x}-1}{x}