## RD Sharma Class 11 Solutions Chapter 29 - Limits (Ex 29.1) Exercise 29.1 - Free PDF

## FAQs on RD Sharma Class 11 Solutions Chapter 29 - Limits (Ex 29.1) Exercise 29.1

**1. What type of questions are given in RD Sharma Class 11 Chapter 29 – Limits (Ex 29.1)?**

The first exercise of RD Sharma Class 11 Chapter 29 consists of questions based on evaluation of left-hand and right-hand limits. There are a total of 22 questions given in the first exercise and students need to solve the questions of this exercise by using the left-hand and right-hand sides of the limit.

**2. Show that \[\lim_{X \rightarrow 0}\frac{X}{\lvert X\rvert}\] does not exist.**

Firstly let us consider L.H.S

\[\lim_{X \rightarrow 0^{-}} = \lgroup\frac{X}{\lvert X\rvert}\rgroup\]

So, let X = 0 - h, where h = 0

\[\lim_{X \rightarrow 0}\frac{X}{\lvert X\rvert}\] = \[\lim_{h \rightarrow 0}\lgroup\frac{0-h}{\lvert 0-h\rvert}\rgroup\]

\[\lim_{h \rightarrow 0} = \lgroup\frac{-h}{h}\rgroup\]

= -1

Now, let us consider the R.H.S

\[\lim_{X \rightarrow 0^{+}} = \frac{\lgroup X\rgroup}{\lvert X\rvert}\]

So, let X = 0 + h, where, h = 0

\[\lim_{X \rightarrow 0} = \frac{\lgroup X\rgroup}{\lvert X\rvert} = \lim_{h \rightarrow 0}= \lgroup\frac{0+h}{\lvert 0+h\rvert}\rgroup\]

\[\lim_{h \rightarrow 0}\lgroup \frac{h}{h}\rgroup\]

= 1

Since L.H.S ≠ R.H.S

∴ Limit does not exist