Mathematics

Mathematics

Problem

Which of the following limits is of indeterminate form ∞∞\dfrac{\infty}{\infty} as x→∞x\to\infty? a) lim⁡x→∞e−xx2\displaystyle\lim_{x\to\infty}\dfrac{e^{-x}}{x^{2}} b) lim⁡x→1x2−1x−1\displaystyle\lim_{x\to 1}\dfrac{x^{2}-1}{x-1} c) lim⁡x→∞ln⁡xx\displaystyle\lim_{x\to\infty}\dfrac{\ln x}{\sqrt{x}} d) lim⁡x→∞arctan⁡xx\displaystyle\lim_{x\to\infty}\dfrac{\arctan x}{\sqrt{x}}

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