Limits And Derivatives class 11 Notes Mathematics

Table of Contents

myCBSEguide App

Download the app to get CBSE Sample Papers 2024-25, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Install Now

CBSE Mathematics Chapter 13 Limits And Derivatives class 11 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Limits And Derivatives class 11 Notes Maths latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 11 Mathematics notes on Chapter 13 Limits And Derivatives class 11 Notes Mathematics are also available for download in CBSE Guide website.

CBSE Guide Limits And Derivatives class 11 Maths Notes

CBSE guide notes are the comprehensive notes which covers the latest syllabus of CBSE and NCERT. It includes all the topics given in NCERT class 11 Mathematics text book. Users can download CBSE guide quick revision notes from myCBSEguide mobile app and my CBSE guide website.

Limits And Derivatives class 11 Notes Mathematics

Download CBSE class 11th revision notes for Chapter 13 Limits And Derivatives class 11 Notes Mathematics in PDF format for free. Download revision notes for Limits And Derivatives class 11 Notes Mathematics and score high in exams. These are the Limits And Derivatives class 11 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.

NCERT solutions for Class 11 Maths Download as PDF

CBSE Class 11 Mathematics Revision Notes Chapter 13 Limits And Derivatives

Limits
Derivatives
Miscellaneous Questions

Meaning of $x \rightarrow a$ or “ $x$ tends to $a$ ” or “ $x$ approaches $a$ “, $x$ is a variable. The expected value of the function as dictated by the points to the left of a point defines the left hand limit of the function at that point. Similarly the right hand limit. It can be changed so that its value comes nearer and nearer to $a$ . $0 < \left| {x - a} \right| < \delta$

(i) $x \ne a$ , (ii) $\left| {x - a} \right|$ becomes smaller and smaller as we please.

Neighbourhood: The set of all real numbers lying between $a - \delta$ and $a + \delta$ is called the neighbourhood of $a$ . Neighbourhood of $a$ = $\left( {a - \delta ,a + \delta } \right),$ $x \in \left( {a - \delta ,a + \delta } \right)$

Limit of a function at a point is the common value of the left and right hand limits, if they coincide

Left hand limit of $f$ at $x = a$ . When $x$ approches $a$ from left hand side of $a$ , the function $f(x)$ tends to $l$ “a definite number”. This definite number $l$ is said to be the left hand limit of $f$ at $x = a$ .

Right hand limit of $f$ at $x = a$ . When $x$ approches $a$ from right hand side of $a$ , the function $f(x)$ tends to $l$ “a definite number”. This definite number $l$ is said to be the right hand limit of at $x = a$ .

Therefore, if Left hand limit of $f$ at $x = a$ = Right hand limit of $f$ at $x = a$ , then the limit of $f(x)$ at $x = a$ exists.

For function f and a real number a, $\underset{x\to \infty }{\mathop{\lim }}\,f(x)$ and f (a) may not be same (Infact, one may be defined and not the other one).
For functions f and g the following holds:.

$\mathop {\lim }\limits_{x \to a} \left[ {f(x) \pm g(x)} \right] =$ $\mathop {\lim }\limits_{x \to a} f(x) \pm \mathop {\lim }\limits_{x \to a} g(x)$

$\underset{x\to a}{\mathop{\lim }}\,\left[ f(x).g(x) \right]=$ $\underset{x\to a}{\mathop{\lim }}\,f(x).\underset{x\to a}{\mathop{\lim }}\,g(x)$

$\underset{x\to a}{\mathop{\lim }}\,\left[ \frac{f(x)}{g(x)} \right]=$ $\frac{\underset{x\to a}{\mathop{\lim }}\,f(x)}{\underset{x\to \infty }{\mathop{\lim }}\,g(x)}$

Following are some of the standard limits

$\underset{x\to a}{\mathop{\lim }}\,\frac{{{x}^{n}}-{{a}^{n}}}{x-a}=n{{a}^{n-1}}$

$\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin x}{x}=1$ , $\mathop {\lim }\limits_{x \to a} {{\sin \left( {x - a} \right)} \over {x - a}} = 1$

$\underset{x\to 0}{\mathop{\lim }}\,\frac{1-\cos x}{x}=0$

$\mathop {\lim }\limits_{x \to 0} {{\tan x} \over x} = 1,$ $\mathop {\lim }\limits_{x \to a} {{\tan \left( {x - a} \right)} \over {x - a}} = 1$

$\mathop {\lim }\limits_{x \to 0} {{{{\sin }^{ - 1}}x} \over x} = 1,$ $\mathop {\lim }\limits_{x \to 0} {{{{\tan }^{ - 1}}x} \over x} = 1$

$\mathop {\lim }\limits_{x \to 0} {{{a^x} - 1} \over x} = {\log _e}a,$ $a > 0,a \ne 1$

Derivatives

The derivative of a function f at a is defined by

$f'(a)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(a+h)-f(a)}{h}$

Derivative of a function f at any point x is defined by

$f'(x)=\frac{df(x)}{dx}=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(x+h)-f(x)}{h}$

For functions u and v the following holds:

$(u\pm v)'=u'\pm v'$

$(uv)'=u'v+uv'$ $\Rightarrow$ ${d \over {dx}}\left( {uv} \right) = u.{{dv} \over {dx}} + v.{{du} \over {dx}}$

${{\left( \frac{u}{v} \right)}^{'}}=\frac{u'v-uv'}{{{v}^{2}}}$ $\Rightarrow$ ${d \over {dx}}\left( {{u \over v}} \right) = {{v.{{du} \over {dx}} - u.{{dv} \over {dx}}} \over {{v^2}}}$

provided all are defind.

Following are some of the standard derivatives

$\frac{d}{dx}({{x}^{n}})=n{{x}^{n-1}}$

$\frac{d}{dx}(\sin x)=\cos x$

$\frac{d}{dx}(\cos x)=-\sin x$

${d \over {dx}}\left( {\tan x} \right) = {\sec ^2}x$

${d \over {dx}}\left( {\cot x} \right) = - \cos e{c^2}x$

${d \over {dx}}\left( {\sec x} \right) = \sec x.\tan x$

${d \over {dx}}\left( {\cos ecx} \right) = - \cos ec{\rm{ }}x.\cot x$

Limits And Derivatives class 11 Notes

CBSE Revision notes (PDF Download) Free
CBSE Revision notes for Class 11 Mathematics PDF
Revision notes Class 11 Maths – CBSE
CBSE Revisions notes and Key Points Class 11 Mathematics
Summary of the NCERT books all chapters in Mathematics class 11
Short notes for CBSE class 11th Mathematics
Key notes and chapter summary of Mathematics class 11
Quick revision notes for CBSE exams

CBSE Class 11 Revision Notes and Key Points

Limits And Derivatives class 11 Notes Mathematics. CBSE quick revision note for class-11 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

To download Limits And Derivatives class 11 Notes, sample paper for class 11 Chemistry, Physics, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through the best app for CBSE students and myCBSEguide website.

Test Generator

Create question paper PDF and online tests with your own name & logo in minutes.

Create Now

myCBSEguide

Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

Install Now

Limits And Derivatives class 11 Notes Mathematics

myCBSEguide App

CBSE Guide Limits And Derivatives class 11 Maths Notes

Limits And Derivatives class 11 Notes Mathematics

CBSE Class 11 Mathematics Revision Notes Chapter 13 Limits And Derivatives

Following are some of the standard limits

Derivatives

Following are some of the standard derivatives

Limits And Derivatives class 11 Notes

CBSE Class 11 Revision Notes and Key Points

Test Generator

myCBSEguide

Related Posts

Leave a Comment