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:

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CBSE CLASS XII Related Questions

1.
Find a point on the line \( \frac{x - 2}{3} = \frac{1 - y}{2} = \frac{z - 3}{2} \) at a distance of \( \sqrt{2} \) units from the point \( (1, 2, 3) \).
View Solution
2.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:
- \(-\frac{\pi}{2}\)
- \(-\frac{\pi}{4}\)
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{2}\)
View Solution
3.
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 :
4.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :
5.
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
6.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]
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.
Find a point on the line \( \frac{x - 2}{3} = \frac{1 - y}{2} = \frac{z - 3}{2} \) at a distance of \( \sqrt{2} \) units from the point \( (1, 2, 3) \).

2.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

4.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :

5.
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 \(q\).

6.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

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.Find a point on the line \( \frac{x - 2}{3} = \frac{1 - y}{2} = \frac{z - 3}{2} \) at a distance of \( \sqrt{2} \) units from the point \( (1, 2, 3) \).

2. Find: The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

4.At a birthday party, children are being served orange juice in conical cups, as shown in the figure. Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.On the basis of the above information, answer the following questions :

5. 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 \(q\).

6. Find: The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Find a point on the line \( \frac{x - 2}{3} = \frac{1 - y}{2} = \frac{z - 3}{2} \) at a distance of \( \sqrt{2} \) units from the point \( (1, 2, 3) \).

2.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

4.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :

5.
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 \(q\).

6.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]