ML Aggarwal Limits and Derivatives ISC Class-11 Maths Understanding

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ML Aggarwal Limits and Derivatives ISC Class-11 Maths Understanding Solutions Chapter-13. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe-1,  Exe-2, Exe-3 Exe-4, Exe-5, Exe-6, and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.

ML Aggarwal Limits and Derivatives ISC Class-11 Maths Understanding Ch-13

Class: 11th
Subject: Mathematics
Chapter  : Ch-13 Limits and Derivatives  Section -A of Vol-II
Board ISC
Writer ML Aggarwal
Publications APC Arya Publications 2020-21

-: Select Topics :- 

Exe-13.1,

 Exe-13.2,

 Exe-13.3,

 Exe-13.4,

 Exe-13.5,

 Exe-13.6,

Chapter Test

ML Aggarwal Limits and Derivatives ISC Class-11 Maths Understanding Ch-13

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;

limy→c

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.

Derivatives

Derivatives are defined as the varying rate of change of a function with respect to an independent variable. The derivative is primarily used when there is some varying quantity, and the rate of change is not constant. The derivative is used to measure the sensitivity of one variable (dependent variable) with respect to another variable (independent variable).Derivatives MeaningDerivatives Maths refers to the instantaneous rate of change of a quantity with respect to the other. It helps to investigate the moment by moment nature of an amount.First-Order DerivativeThe first order derivatives tell about the direction of the function whether the function is increasing or decreasing. The first derivative math or first-order derivative can be interpreted as an instantaneous rate of change. It can also be predicted from the slope of the tangent line.Second-Order DerivativeThe second-order derivatives are used to get an idea of the shape of the graph for the given function. The functions can be classified in terms of concavity. The concavity of the given graph function is classified into two types namely:

  1. Concave Up
  2. Concave Down.

Exe-13.1

ML Aggarwal Limits and Derivatives ISC Class-11 Maths Understanding Ch-13

Exe-13.2

ML Aggarwal Limits and Derivatives ISC Class-11 Maths Understanding Ch-13

Exe-13.3

ML Aggarwal Limits and Derivatives ISC Class-11 Maths Understanding Ch-13

Limit:

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).

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.

Exe-13.4

ML Aggarwal Limits and Derivatives ISC Class-11 Maths Understanding Ch-13

Exe-13.5

 Limits and Derivatives ISC Class-11 Maths Understanding Ch-13

Exe-13.6

ML Aggarwal Limits and Derivatives ISC Class-11 Maths Understanding Ch-13

Chapter Test

ML Aggarwal Limits and Derivatives ISC Class-11 Maths Understanding Ch-13

-: End of Limits and Derivatives ISC Class-11 ML Aggarwal Maths Understanding Chapter-13 Solution :-

Return to :- ML Aggrawal ISC Class-11 APC Understanding Maths Solutions

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