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
