nubtrek

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.continue

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. continue

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.

continue

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. continue

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. continue

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. continue

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. continue

summary of this topic

Limit of Algebraic Expressions

Limit of Algebraic Expressions

Voice  

Voice  



Home



Limit of Polynomials


Apply Algebra of Limits
For a function `f(x) = a_nx^n``+a_(n-1)x^(n-1)``+ cdots ``+ a_1x^1 ``+ a_0`

`lim_(x->a) f(x) `

`quad quad = a_n lim_(x->a) x^n``+a_(n-1) lim_(x->a) x^(n-1)``+ cdots ``+ a_1 lim_(x->a) x^1 ``+ a_0`

Limit of Polynomials

plain and simple summary

nub

plain and simple summary

nub

dummy

Limit of a polynomial is the limit on individual terms of the polynomial.

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.




Finding limit of standard polynomial expressions is explained with an example.


Keep tapping on the content to continue learning.
Starting on learning "limit of polynomials". ;; Finding limit of standard polynomial expressions is explained with an example.

How to find limits of function `f(x)=3x^3+2x^2-1` at `x=-2`

  • apply limit to the three terms of the function
  • one has to memorize a formula

The answer is 'apply limit to the three terms of the function'

limit of function `f(x)=color(deepskyblue)(3x^3)+color(coral)(2x^2)-1` at `x=-2`

By Substitution :
`f(x)|_(x=-2)`
`quad quad = color(deepskyblue)(3(-2)^3)+color(coral)(2(-2)^2)-1`
`quad quad = color(deepskyblue)(3(-8))+color(coral)(2(4))-1`
`quad quad = -17`

limits of function `f(x)=color(deepskyblue)(3x^3)+color(coral)(2x^2)-1` at `x=-2`

left-hand-limit :
`lim_(x->-2-)f(x)`
`quad quad = color(deepskyblue)(3(-2-delta)^3)+color(coral)(2(-2-delta)^2)-1`
substitute `delta=0`
`quad quad = color(deepskyblue)(3(-8))+color(coral)(2(4))-1`
`quad quad = -17`

limits of function `f(x)=color(deepskyblue)(3x^3)+color(coral)(2x^2)-1` at `x=-2`

right-hand-limit :
`lim_(x->-2+)f(x)`
`quad quad = color(deepskyblue)(3(-2+delta)^3)+color(coral)(2(-2+delta)^2)-1`
substitute `delta=0`
`quad quad = color(deepskyblue)(3(-8))+color(coral)(2(4))-1`
`quad quad = -17`

limits of function `f(x)=3x^3+2x^2-1` at `x=-2`

`f(x)|_(x=-2) = -17`

`lim_(x->-2-)f(x)= -17`

`lim_(x->-2+)f(x)= -17`

All three values are equal. So the function is continuous.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Limit of a polynomial: For a function `f(x) = a_nx^n+a_(n-1)x^(n-1)+ cdots + a_1x^1 + a_0`
`lim_(x->a) f(x) `
`quad quad = a_n lim_(x->a) x^n+a_(n-1) lim_(x->a) x^(n-1)+ cdots `
`quad quad quad quad + a_1 lim_(x->a) x^1 + a_0`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

your progress details

Progress

About you

Progress

How to find limits of function f of x equals 3 x cube + 2 x squared minus 1 at x = minus 2 ?
apply;limit;3;terms
apply limit to the three terms of the function
one;has;memorize;
one has to memorize a formula
The answer is 'apply limit to the three terms of the function'
limits of function f of x = 3 x cube + 2 x squared minus 1 at x = minus 2 ;; by substitution : f of x at x equal minus 2;; equals 3 into minus 2 cubed + 2 into minus 2 squared minus 1;; equals 3 into minus 8 + 2 into 4 minus 1;; equals minus 17.
limits of function f of x = 3 x cube + 2 x squared minus 1 at x = minus 2 ;; left hand limit equals 3 into minus 2 minus delta cubed + 2 into minus 2 minus delta squared minus 1;; substitute delta = 0;; equals 3 into minus 8 + 2 into 4 minus 1;; equals minus 17.
limits of function f of x = 3 x cube + 2 x squared minus 1 at x = minus 2 ;; right hand limit equals 3 into minus 2 plus delta cubed + 2 into minus 2 plus delta squared minus 1;; substitute delta = 0;; equals 3 into minus 8 + 2 into 4 minus 1;; equals minus 17.
Limits of function f of x = 3 x cube + 2 x squared minus 1 at x = minus 2;; f of x at x = minus 2, = minus 17;; limit x tending to minus 2 minus, f of x = minus 17;; limit x tending to minus 2 plus, f of x = minus 17;; All the three values are equal. So the function is continuous.
Limit of a polynomial is the limit on individual terms of the polynomial.
Limit of a polynomial is the limit on individual terms of the polynomial. This is given in mathematical form.

we are not perfect yet...

Help us improve