Limits and Derivatives — MATHS STD 11 Science — Question

4. does not exist

Solution:

Using,

$ \lim_\limits{\text{x} \rightarrow 0}|\text{x}|=-\text{x}$

$ \lim_\limits{\text{x} \rightarrow 0}|\text{x}|=+\text{x}$

we get $\lim_\limits{\text{x} \rightarrow \text{a}}-\frac{\text{x}-\text{a}}{-(\text{x}-\text{a})}=-1$

$\lim_\limits{\text{x} \rightarrow \text{a}}+\frac{\text{x}-\text{a}}{-(\text{x}-\text{a})}=-1$

Since, LHL is not equal to RHL, hence the limit does not exist.