What is the limit as x approaches infinity of e^{1/2-1/(x^2)}-1 ?

The limit as x approaches infinity of e^{1/2-1/(x^2)}-1 is sqrt(e)-1

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limit as x approaches infinity of e^{1/2-1/(x^2)}-1

x \to \infty lim (e^{\frac{1}{2} - \frac{1}{x ^{2}}} - 1)

e - 1

Decimal Notation

0.64872 \dots

Solution steps

x \to \infty lim (e^{\frac{1}{2} - \frac{1}{x ^{2}}} - 1)

Simplify

e^{\frac{1}{2} - \frac{1}{x ^{2}}} : e^{- \frac{1}{x ^{2}}} e

= x \to \infty lim (e^{- \frac{1}{x ^{2}}} e - 1)

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim (e^{- \frac{1}{x ^{2}}} e) - x \to \infty lim (1)

x \to \infty lim (e^{- \frac{1}{x ^{2}}} e) = e

x \to \infty lim (1) = 1

= e - 1

n = 1 \sum \infty 1 (\frac{1}{6})^{n}

n = 1 \sum \infty n^{n} (x - 3)^{n}

\int_{0}^{\frac{π}{2}} \frac{cos ( θ )}{1 + sin ( θ )} d θ

n = 0 \sum \infty 2 (\frac{- 2}{3})^{n}

\frac{d y}{d x} = e^{- (x + y)}

What is the limit as x approaches infinity of e^{1/2-1/(x^2)}-1 ?
The limit as x approaches infinity of e^{1/2-1/(x^2)}-1 is sqrt(e)-1