Function Expression :
\[f(x)=x+\sqrt{1-x^2} \]Domain
\[\left[-1, 1\right] \]Limits
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = -1 \]\[\lim_{x \overset{<}{\rightarrow1} }f(x) = 1 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- \frac{x}{\sqrt{1 - x^{2}}} + 1 \]\[f^{\,\prime}(x)=\frac{- x + \sqrt{1 - x^{2}}}{\sqrt{1 - x^{2}}} \]
Integral
\[F(x) = \frac{x^{2}}{2} + \frac{x \sqrt{1 - x^{2}}}{2} + \frac{\operatorname{asin}{\left(x \right)}}{2} \]Sign Table
Variation Table
Plot
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