RD Sharma Class 11 Maths Solutions Chapter 29 - Limits

Limits, and the RD Sharma Solutions on this page provide answers to the questions in each exercise. Let's take a closer look at the principles covered in this chapter.

• Limiting in a non-formal way.

• Limits of the left and right hands are assessed.

• The difference between a function's value and its limit at a given point.

• The mathematics of limits.

• Limits evaluation and indeterminate forms

• Limits in algebra are evaluated.

1. Method of direct substitution.

2. Factorization is a type of factorization.

3. Method of rationalisation.

4. Standard limits are used to evaluate algebraic limits.

5. At infinity, there is a method for evaluating algebraic limits.

• Limits of trigonometry are evaluated.

1. When a variable approaches 0, trigonometric limits are evaluated.

2. When variables trend to a non-zero amount, trigonometric limits are evaluated.

3. Factorization is used to evaluate trigonometric limits.

• Limits of exponential and logarithmic magnitude are evaluated.

For example

PAGE NO: 29.11 EXERCISE 29.1

17.  Show that \[\lim_{x\rightarrow 0}\frac{X}{|X|}\] does not exist.

Solution:

Firstly let us consider LHS:

\[\lim_{x\rightarrow 0^{-}}\left(\frac{x}{|x|}\right)\]

So let x = 0-h where h=0

\[\lim_{x\rightarrow 0}\frac{(X)}{|X|}\] = \[\lim_{h\rightarrow 0}\left(\frac{0 - h}{|0 - h|}\right)\]

= \[\lim_{h\rightarrow 0}\left(\frac{-h}{h}\right)\]

= -1

Now let’s consider rhs 

\[\lim_{x\rightarrow 0^{+}}\frac{(x)}{|x|}\]

x=0+h where h=0

\[\lim_{x\rightarrow 0^{+}}\frac{(x)}{|x|}\]

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

\[\lim_{x\rightarrow 0}\frac{(X)}{|X|}\] = \[\lim_{h\rightarrow 0}\left(\frac{0 + h}{|0 + h|}\right)\]

= \[\lim_{h\rightarrow 0}\left(\frac{h}{h}\right)\]

= 1

since rhs is not equal to lhs limit does not exist 

Class 11 RD Sharma's Exam Preparation Tips Using Limits and Derivatives

Limits and Derivatives Class 11 RD Sharma can be solved using the free PDF accessible on the Vedantu platform. When preparing RD Sharma Limits and Derivatives answers, students should keep the following ideas in mind.

• Before attempting the questions, students should read them attentively. Because the questions from Limits and Derivatives contain a few tough issues, we may end up with the incorrect answer if the questions are not fully comprehended.

• The free PDF on the Vedantu site walks you through a solution step by step. As a result, students are recommended to go through the material properly and not skip any procedures.

• There are several exercise problems and practice problems in the RD Sharma Solutions Class 11 Chapter 29 that assist students to prepare for their exams.

The following are some of the important concepts of limits and derivatives discussed in this chapter:

• Derivatives: An Intuitive Concept

• Examples are used to limit the definition.

• Limits algebra.

• Polynomial and rational function limits

• Trigonometric Functions' Limits

• Derivatives

• Algebra of function derivatives

• Polynomial derivatives and trigonometric functions

Students will feel more secure when trying any Limits and Derivatives questions after studying RD Sharma Class 11 Solutions Chapter 29. The free PDF on RD Sharma solutions is created by talented experts to provide students with top-notch, error-free solutions. Students can get a free copy of the PDF document from Vedantu's portal.