Function Expression :
\[f(x)=sin(\frac{x+1}{2x+1} ) \]Domain
\[\left]-\infty, - \frac{1}{2}\right[ \cup \left]- \frac{1}{2}, \infty\right[ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = \sin{\left(\frac{1}{2} \right)} \]\[\lim_{x \overset{<}{\rightarrow- \frac{1}{2}} }f(x) = \left\langle -1, 1\right\rangle \]
\[\lim_{x \overset{>}{\rightarrow- \frac{1}{2}} }f(x) = \left\langle -1, 1\right\rangle \]
\[\lim_{x \rightarrow+\infty}f(x) = \sin{\left(\frac{1}{2} \right)} \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\left(- \frac{2 \left(x + 1\right)}{\left(2 x + 1\right)^{2}} + \frac{1}{2 x + 1}\right) \cos{\left(\frac{x + 1}{2 x + 1} \right)} \]\[f^{\,\prime}(x)=- \frac{\cos{\left(\frac{x + 1}{2 x + 1} \right)}}{\left(2 x + 1\right)^{2}} \]
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Integral
\[F(x) = \int \sin{\left(\frac{x + 1}{2 x + 1} \right)}\, dx \]Sign Table
Variation Table
Plot
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