Solution: The given function $f(x)=|x|+|x-1|$ A function $f(x)$ is said to be continuous on a closed interval $[a, b]$ if and only if, (i) $\mathrm{f}$ is continuous on the open interval...

Solution: The given function $f(x)=\left\{\begin{array}{c}\left(x^{3}-x^{2}+2 x-2\right), \text { if } x \neq 1 \\ 4, \text { if } x=1\end{array}\right.$ L.H.L. at $\mathrm{x}=1: \lim _{\mathrm{x}...

Solution: The given function is $f(x)=\left\{\begin{array}{l}x, \text { if } x \neq 0 \\ 1, \text { if } x=0\end{array}\right.$ L.H.L. at $\mathrm{x}=0$ $\lim _{x \rightarrow 0^{-}} f(x)=\lim _{h...

Solution: The given function $f(x)=\left\{\begin{array}{c}(2 x-1), \text { if } x<2 \\ \frac{3 x}{2}, \text { if } x \geq 2\end{array}\right.$ L.H.L. at $x=2$ $\lim _{x \rightarrow 2^{-}}...

Solution: It is known that $\sin x$ is continuous everywhere Now considering the point $x=0$ L.H.L: $\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{-}}\left(\frac{\sin x}{x}\right)=\lim...

Solution: Assume $f(x)=\sec |x|$ and a be any real number. Then, L.H.L. at $\mathrm{x}=\mathrm{a}$ $\lim _{x \rightarrow \mathrm{a}^{-}} \mathrm{f}(\mathrm{x})=\lim _{\mathrm{x} \rightarrow...

Solution: It is given that: $f(x)=\left\{\begin{array}{l} (7 x+5), \text { when } x \geq 0 \\ (5-3 x), \text { when } x<0 \end{array}\right.$ Let us now calculate the limit of $f(x)$ when $x$...