Function Expression :
\[f(x)=\frac{\sqrt{x^2+1}-1}{x} \]Domain
\[\left]-\infty, 0\right[ \cup \left]0, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = -1 \]\[\lim_{x \overset{<}{\rightarrow0} }f(x) = 0 \]
\[\lim_{x \overset{>}{\rightarrow0} }f(x) = 0 \]
\[\lim_{x \rightarrow+\infty}f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{1}{\sqrt{x^{2} + 1}} - \frac{\sqrt{x^{2} + 1} - 1}{x^{2}} \]\[f^{\,\prime}(x)=\frac{1}{x^{2}} - \frac{1}{x^{2} \sqrt{x^{2} + 1}} \]
\[f^{\,\prime}(x)=\frac{\sqrt{x^{2} + 1} - 1}{x^{2} \sqrt{x^{2} + 1}} \]
Integral
\[F(x) = \sqrt{x^{2} + 1} - \log{\left(\sqrt{x^{2} + 1} + 1 \right)} \]Sign Table
Variation Table
Plot
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