NCERT Solutions For Class 11 Maths Chapter 13: Limits and Derivatives

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NCERT Solutions for class 11 Maths Chapter 13 Limits and Derivatives are provided in the article. A limit is defined as a value that a function approaches as the input, and it produces some value. A derivative refers to the instantaneous rate of change of a quantity with respect to the other. NCERT Solutions for class 11 Maths Chapter 13 cover following important concepts:

Download: NCERT Solutions for Class 11 Mathematics Chapter 13 pdf

Class 11 Maths NCERT Solutions Chapter 13 Limits and Derivatives

Class 11 Maths NCERT Solutions Chapter 9 Limits and Derivatives are provided below:

Also read: Important Questions Limits and Derivatives

Important Topics for Class 11 Maths NCERT Solutions Chapter 13 Limits and Derivatives

Important Topics for Class 11 Maths NCERT Solutions Chapter 13 Limits and Derivatives are elaborated below:

Limits

Limits are values that a function (or sequence) approaches as the input (or index) approaches some value. Limits are important in calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.

Derivatives

Derivative, in mathematics, is the rate of change of a function with respect to a variable. Derivatives are the basic solutions of problems in calculus and differential equations.

List of Limits and Derivatives Class 11 Formulas

d/dx [f(x) + g (x)] = d/dx [f(x)] + d/dx [g(x)]
d/dx [f(x) - g (x)] = d/dx [f(x)] - d/dx [g(x)]
d/dx [f(x) * g (x)] = d/dx [f(x)]*[g(x)] + [f(x)]*d/dx [g(x)]
d/dx [f(x) / g (x)] = {d/dx [f(x)]*[g(x)] - [f(x)]*d/dx [g(x)]} / g(x)²
lim_x → a(xⁿ - aⁿ) / x - a = na^n-1
lim_^x → a sinx / x = 1
limx → a¹ - cosx / x = 0
f ´( x ) = d f(x)/dx = lim_h → 0 [ f(x+h) - f(x) / h]

NCERT Solutions For Class 11 Maths Chapter 13 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 13 Limits and Derivatives under different exercises are as follows:

Also Check:

Chapter Related Topics
Derivative of Inverse Trigonometric Function	Value of Log Infinity	Ln and Log

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CBSE CLASS XII Related Questions

1.
Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).
- Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
View Solution
2.
A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.
View Solution
3.
Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not.
View Solution
4.
Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not.
View Solution
5.
Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]
View Solution
6.
Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]
View Solution

View All

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NCERT Solutions For Class 11 Maths Chapter 13: Limits and Derivatives

Class 11 Maths NCERT Solutions Chapter 13 Limits and Derivatives

Important Topics for Class 11 Maths NCERT Solutions Chapter 13 Limits and Derivatives

CBSE CLASS XII Related Questions

1.
Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

2.
A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.

3.
Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not.

4.
Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not.

5.
Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]

6.
Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]

Similar Mathematics Concepts

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NCERT Solutions For Class 11 Maths Chapter 13: Limits and Derivatives

Class 11 Maths NCERT Solutions Chapter 13 Limits and Derivatives

Important Topics for Class 11 Maths NCERT Solutions Chapter 13 Limits and Derivatives

CBSE CLASS XII Related Questions

1.Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \). Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

2. A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.

3.Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not.

4.Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not.

5. Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]

6. Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

2.
A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.

3.
Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not.

4.
Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not.

5.
Evaluate: \[ \cos\left[\sin^{-1}(-1)-\tan^{-1}(-\sqrt{3})\right]. \]

6.
Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]