OP Malhotra Class-11 **Limits** S.Chand ISC Maths Solution Chapter-18. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-18 (a), 18 (b), 18 (c), 18 (d), 18 (e), 18 (f), 18 (g), 18 (h), 18 (i), 18 (j), With Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## OP Malhotra Class-11 Limits S.Chand ISC Maths Solution

Class: | 11th |

Subject: | Mathematics |

Chapter : | Ch-18 Limits of Section -A |

Board | ISC |

Writer | OP Malhotra |

Publications | S.Chand Publications 2020-21 |

–: Select Topics :-

### OP Malhotra Class-11 Limits S.Chand ISC Maths Solution

**Limits Definition**

A limit of a function f(x) is defined as a value, where the function reaches as the limit reaches some value. Limits are used to define integration, integral calculus and continuity of the function.

If f(y) is a function, then the limit of the function can be represented as;

lim_{y→c}

This is the general expression of limit, where c is any constant value. But there are some important properties of limits which we will discuss here.

- When we say that x approaches a (x → a) then we mean that the variable x takes those values which are either less than ‘a’ or greater than ‘a’ and the numerical difference between ‘x’ and ‘a’ can be made as small as we please

OR

Let y = f(x) be a function of x. If at x = a, f(x) takes indeterminate form, then we consider the values of the function which is very near to a. If these value tend to a definite unique number as x tends to a, then the unique number so obtained is called the limit of f(x) at x = a and we write it as lim𝑥→𝑎𝑓(𝑥).

**Limits**

**l** is called the limit of the function **f(x)** if the equation is given as **x → a, f(x) → l**, and this is symbolically written for all the limits, the function should assume at a given point x = a. **x** could approach a number in two ways, either from the left or from the right, i.e., all the values of** x** near **a **could be greater than **a **or could be less than** a**.

**Right-Hand Value**

In this type of limits, Right-hand limit Value is referred to the situation in which **f(x)** gets dictated by values of **f(x)** when **x** tends to from the right.

**What is a Left-Hand Value?**

In the case of Left-hand limit, when **x **tends to from the left, the value of **f(x)** gets dictated by values of **f(x)**.

In this case, the right and left-hand limits are different, and hence we say that the limit of **f(x)** as **x** tends to zero does not exist (even though the function is defined at **0**). This could also be followed in limits and continuity of values.

- Concave Up
- Concave Down.

Exe-18 (a)

### OP Malhotra Class-11 Limits S.Chand ISC Maths Solution

Page 18-8

### Exe-18 (b)

OP Malhotra Class-11 Limits S.Chand ISC Maths Solution

Page 18-11

Exe-18 (c)

### Class-11 Limits S.Chand ISC Maths Solution

Page 18-13

### Exe-18 (d)

OP Malhotra Class-11 Limits S.Chand ISC Maths Solution

Page 18-15

Exe-18 (e)

### OP Malhotra Limits S.Chand ISC Maths Solution

Page 18-18

Exe-18 (f)

### OP Malhotra Class-11 Limits S.Chand ISC Maths Solution

Page 18-22

### Exe-18 (g)

OP Malhotra Class-11 Limits S.Chand ISC Maths Solution

Page 18-27

Exe-18 (h)

### OP Malhotra Class-11 S.Chand ISC Maths Solution

Page 18-31

### Exe-18 (i)

OP Malhotra Class-11 Limits S.Chand ISC Maths Solution

Page 18-35 to 18-36

### Exe-18 (j)

Class-11 Limits S.Chand ISC Maths Solution

Page 18-38 to 18-39

Chapter Test

### OP Malhotra Class-11 Limits S.Chand ISC Maths Solution

Page 18-39

-: End of **Limits** Solution :-

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