Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.

User Guide

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
think,
figure-out, &
learn.

Just keep tapping (or clicking) on the content to continue in the trail and learn.

User Guide

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about.

User Guide

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step.

User Guide

jogger provides the complete mathematical definition of the concepts.

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen.

User Guide

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

### Algebra of Limits

Voice

Voice

Home

Understanding Algebra of Limits

»  Finding limit of function as sub-expressions

→  f(x) +- g(x)

→  f(x) xx g(x)

→  f(x) -: g(x)

→  [f(x)]^n

→  f(x) and y=g(x)

»  Algebra of Limits

→  If sub-expressions are not evaluating to 0 or oo then limit can be applied to sub-expressions.

→  If sub-expressions are evaluating to 0 or oo, then look for the forms of 0/0.

### Algebra of Limits : Introduction

plain and simple summary

nub

plain and simple summary

nub

dummy

Algebra of limits helps to simplify finding limit by applying the limit to sub-expressions of a function.
Algebra of limits may not be applicable to the sub-expressions evaluating to 0 or oo or at discontinuities.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

Support Nubtrek

You are learning the free content, however do shake hands with a coffee to show appreciation.
To stop this message from appearing, please choose an option and make a payment.

This topic explains the observations one has to take before applying algebra of limits.

Keep tapping on the content to continue learning.
Starting on learning "Introduction to Algebra of Limits". ;; This topic explains the observations one has to take before applying algebra of limits.

What does "Algebra of limits" mean?

• Properties to find limit of functions given as algebraic operations of several functions
• Applying limit in practical applications

The answer is 'Properties to find limit of functions given as algebraic operations of several functions'

The basic mathematical operations are
•  multiplication and division
•  powers and roots.

Two or more function g(x) h(x) can form another function f(x).
f(x) = g(x) *** h(x) quad quad where *** is one of the mathematical operations.

Will there be any relationship between the limits of the functions lim g(x) ; lim h(x) and the limit of the function lim f(x)?
Algebra of limits analyses this and provides the required knowledge.

In computing limit of a function, when does value of the function or limit of the function change?

• when a function evaluates to 0 in denominator
• When a function evaluates to oo
• at the discontinuous points of piecewise functions
• all the above

The answer is 'all the above'

When applying algebra of limits to elements of a function, look out for the following cases.

•  Expressions evaluating to 1/0 or 0/0 or oo xx 0 or oo / oo

eg: 1/(x-1), (x^2-1)/(x-1), tan x cot x, (tan x)/(sec x)

•  Expressions evaluating to oo - oo or oo + (-oo)
eg: (x^2-4x)/x - 1/x
•  discontinuous points of piecewise functions

eg: {(1, quad if quad x>0),(0, quad if quad x<=0) :}

The algebra of limit applies only when the above values do not occur.

Example:
lim_(x->1) color(deepskyblue)(x^2-1)/color(coral)(x-1)
quad quad != color(deepskyblue)(lim_(x->1) (x^2-1))/color(coral)(lim_(x->1)(x-1) )
The above is not applicable because it evaluates to 0/0.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Algebra of Limits: If a function f(x) consists of mathematical operations of sub-expressions f_1(x), f_2(x), etc. then the limit of the function can be applied to the sub-expressions.

If any of the sub-expressions or combination of them evaluate to 0 or oo then, the algebra of limit may not be applied to those sub-expressions.

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Progress

Progress

What does "Algebra of limits" mean?
find;given;algebraic;several
Properties to find limit of functions given as algebraic operations of several functions
practical;applications;applying
Applying limit in practical applications
The answer is 'Properties to find limit of functions given as algebraic operations of several functions'
The basic mathematical operations are ;; addition and subtraction ;; multiplication and division ;; powers and roots. ;; Two or more function g of x , h of x can form another function f of x .;; f of x = g of x star h of x ; where star is one of the mathematical operations. ;; Will there be any relationship between the limits of the functions limit g of x ; limit h of x and the limit of the function limit f of x ? ;; Algebra of limits analyses this and provides the required knowledge.
In computing limit of a function, when does value of the function or limit of the function change?
0;denominator
when a function evaluates to 0 in denominator
infinity
When a function evaluates to infinity
discontinuous;piecewise;points
at the discontinuous points of piecewise functions
all;above
all the above
The answer is 'all the above'
When applying algebra of limits to elements of a function, look out for the following cases. ;;Expressions evaluating to 1 by 0, or 0 by 0, or infinity into 0, or infinity by infinity ;;for example: 1 by x minus 1, x squared minus 1 by x minus 1 , tan x cot x , tan x by sec x ;; Expressions evaluating to infinity minus infinity, or infinity plus minus infinity ;; for example: x squared minus 4x by x, minus 1 by x ;; discontinuous points of piecewise functions;; for example : 1 if x greater than 0, 0 if x less than equal to 0 ;; The algebra of limit applies only when the above values do not occur. ;; Example: limit x tending to 1 x squared minus 1 by x minus 1;; is not equal to, limit x tending to 1, x squared minus 1 as numerator divided by, limit x tending to 1, x minus 1 as denominator;; The above is not applicable because it evaluates to 0 by 0.
Algebra of limits helps to simplify finding limit by applying the limit to sub-expressions of a function.;; Algebra of limits may not be applicable to the sub-expressions evaluating to 0, or infinity, or at discontinuities.
Algebra of Limits: If a function f of x consists of mathematical operations of sub-expressions f 1 of x , f 2 of x, etc. then the limit of the function can be applied to the sub-expressions. ;; If any of the sub-expressions or combination of them evaluate to 0 or infinity then, the algebra of limit may not be applied to those sub-expressions.

we are not perfect yet...