fun-lim

Related Questions

• $\underset{x\to 0}{\mathop{\lim }}\,\frac{1-\cos x}{{{\sin }^{2}}x}=$

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• If X and Y are two non- empty sets where $f:X\to Y$is function is defined such that $f(c)=\left\{ f(x):x\in C \right\}$for $C\subseteq X$and ${{f}^{-1}}(D)=\{x:f(x)\in D\}$for $D\subseteq Y$ for any $A\subseteq X$ and $B\subseteq Y,$then

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• If $f(x) = \begin{cases} x,\;\;\;\,\,{\rm{when}}\;x > 1\\ {x^2},\,\,\,{\rm{when}}\,\,x < 1 \end{cases}$, then $\underset{x\to 1}{\mathop{\lim }}\,f(x)=$

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• $\underset{x\to 0}{\mathop{\lim }}\,\frac{{{y}^{2}}}{x}=........$ , where ${{y}^{2}}=ax+b{{x}^{2}}+c{{x}^{3}}$

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• If $f(x) = \begin{cases} \sin x,x \ne n\pi ,n \in Z\\ \,\,\,\,\,\,0,\,\,{\rm{otherwise}} \end{cases}$ and $g(x) = \begin{cases} {x^2} + 1,x \ne 0,\,2\\ \,\,\,\,\,\,\,\,4,x = 0\\ \,\,\,\,\,\,\,\,\,5,x = 2 \end{cases}$ then $\underset{x\to 0}{\mathop{\lim }}\,g\{f(x)\}=$

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