Limits and Derivatives: Overview, Questions, Preparation

1.8K Views

This chapter has multiple topics listed below:

Limits and Derivatives Derivatives Limits L Hospital Rule Quotient Rule Indeterminate Forms Limits and Continuity

Rachit Kumar SaxenaManager-Editorial

Updated on Aug 13, 2021 14:10 IST

Table of Contents

What are Limits and Derivatives?
Weightage of Limits and Derivatives
Illustrated Examples on Limits and Derivatives
FAQs on Limits and Derivatives

What are Limits and Derivatives?

Based on his theories of rate and change, Sir Isaac Newton set out simple laws about differential and integral calculus. The principles of distinction and calculus act as the basis for many advanced areas such as advanced algebra, mechanics, engineering, and research. Limits and derivatives are scientifically vital principles of Maths but are still applied in other topics such as Physics.

A Function's Limits

A limit is a value at which a function will get to as the input, and what it will generate as the output. Limits are imperative.
lim_n→c f(n)=L

A Function's Derivatives

A derivative refers to the rate of change of a quantity with respect to another and is called a second derivative. It helps to investigate the essence of an amount at the moment of its incidence. The derivative is found in the formula below the expression.
lim_h→0{ f(x+h)-f(x)}/h

Features of Derivatives

The properties of certain derivatives are defined below.

For the function f, its derivative is referred to as f'(x) because there is some equation indicating that f' exists. You can look up all the derivative formulas in the mathematics section here.

Components of limits

Let x be a value such that lim (x → a) (x → b) exists.

Weightage of Limits and Derivatives

This concept is taught under Limits And Derivatives. You will learn the formula and the application of limits and derivatives for solving questions. The weightage of this chapter is 5 marks.

Illustrated Examples on Limits and Derivatives

1. Find lim_x→3(x+3)

Solution.

lim_x→3(x+3) = 3+3 = 6

2.Find the derivative of the sin x at x = 0.

Solution:

Say, f(x) = sin x

then, f'(0) = lim_h→0[f(0+h) – f(0)]/h

= lim_h→0[sin(0+h) – sin(0)]/h

= lim_h→0[sin h]/h

= 1

FAQs on Limits and Derivatives

Q: What is a limit?

A: Limits define how a function performs near the point but does not have the feature near the point. The influence of calculus is the core principle used in calculus.

Q: What is a derivative?

A: Derivatives are found in calculus. The derivative of a real variable parameter quantifies how the quantity is influenced by modifying the independent variable.

Q: Why do we use limits and derivatives?

A: A derivative refers to the rate of change of a quantity with respect to another and is called a second derivative. It helps to investigate the essence of an amount at the moment of its incidence. A limit is a value at which a function will get to as the input, and what it will generate as the output. Limits are used in calculus and mathematical analysis to describe limits, continuity, and derivatives.

Q: What are the examples of limits in everyday life?

A: Examples of limits are the diameter of an ice cube in a bottle of warm water and the weight of a spoon. Other examples, including calculating electric, magnetic or gravitational fields, will be mentioned. The real-world limits are used anytime, and wherever where, a practical solution is found.

Q: What is the derivative's use?

A: Derivatives may be used to place values on functions and/or repeat infinite series. They may be used to show that a function is increasing or declining by the rate of transition. They have a number of applications in physics.