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

Also check:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Arithmetic

CBSE CLASS XII Related Questions

1.
Find:

If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of $p$ and $q$.
- $p = -\frac{2}{3}, \, q = \frac{5}{3}$
- $p = -\frac{8}{3}, \, q = \frac{20}{3}$
- $p = \frac{20}{3}, \, q = -\frac{8}{3}$
- $p = 0, \, q = 0$
View Solution
2.
Which of the following equations is NOT a Linear Differential Equation?
- $(1 + x^2) \, dy + 2xy \, dx = \cot x \, dx$
- $y + \frac{d}{dx}(xy) = x(\sin x + \log x)$
- $x(1 + y^2) \, dx - y(1 + x^2) \, dy = 0$
- $y \, dx - (x + 3y^2) \, dy = 0$
View Solution
3.
Evaluate:
\[ \int_{0}^{1} \frac{x \tan^{-1}x}{(1+x^2)^{3/2}}\,dx \]
View Solution
4.
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.
Based on the above information, answer the following questions :
5.
Find:
Let $A=[a_{ij}]$ be a $2\times2$ matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix $A'$.
- $\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}$
- $\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}$
- $\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}$
- $\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}$
View Solution
6.
A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is
- Reflexive only
- Reflexive and Transitive
- Symmetric and Transitive
- Symmetric only
View Solution