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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

### Calculating Limits

Voice

Voice

Home

Limit of Function with abrupt change

»  A function f(x) at x=a is
→  continuous: if f(a) = LHL = RHL

### Limit of functions with abrupt change

plain and simple summary

nub

plain and simple summary

nub

dummy

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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With an example, calculation of limits for a function with special property is discussed.

Keep tapping on the content to continue learning.
Starting on learning "Limit of functions with abrupt change". ;; With an example, calculation of limits for a function with special property is discussed.

Given function f(x)=|x-1|. what is f(x)|_(x=1)?

• 0
• -1
• +1

The answer is '0'

Given function f(x)=|x-1|. what is left-hand-limit lim_(x->1-)f(x)?

• 0
• -1
• +1

The answer is '0'

Given function f(x)=|x-1|. what is right-hand-limit lim_(x->1+)f(x)?

• 0
• -1
• +1

The answer is '0'

Given function f(x)=|x-1|.

•  f(1)=0

•  lim_(x->1-)f(x) = 0

•  lim_(x->1+)f(x) = 0
The function is continuous at x=1. Note that the function undergoes an abrupt change at x=1.

•  for x<1, the slope of the line is -1

•  for x>1, the slope of the line is 1

•  At x=1, the slope of the line is not defined.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given the function f(x)=|sin x|. Is the function continuous or defined at x=pi?

• continuous
• defined and not continuous
• not defined and not continuous

Progress

Progress

Given function f of x = mod x minus 1. What is f of x at x =1?
0
0
-1;minus
minus 1
plus
plus 1
Given function f of x = mod x minus 1. What is left-hand-limit limit x tending to 1 minus, f of x?
0
0
-1;minus
minus 1
plus
plus 1
Given function f of x = mod x minus 1. What is right-hand-limit limit x tending to 1 +, f of x?
0
0
-1;minus
minus 1
plus
plus 1