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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

Examining Function at an input Value

»  A function f(x) at x=a is

→  continuous: if f(a) = LHL = RHL

→  defined by value: if f(a) is a real number

→  defined by limit: if f(a)=0/0 and LHL = RHL

→  not defined: if LHL != RHL and f(a) !in RR

### Examining Function at an input value

plain and simple summary

nub

plain and simple summary

nub

dummy

Whether a function is continuous or defined or not defined is determined by examining
• value at the input value,

• left-hand-limit at the input value, and

• right-hand-limit at the input value.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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Revising the basics learned in earlier lesson and summarizing the understanding.

Keep tapping on the content to continue learning.
Starting on learning "Examining function at an input value". ;; Revising the basics learned in earlier lesson and summarizing the understanding.

A function f(x) is examined at an input value x=a. Which of the following is to be examined?

• f(a)
• left-hand-limit
• right-hand-limit
• all the above

The answer is 'all the above'.

It is important to note that the L'Hospital's rule is applicable only if the limit exists. The discussion in this topic is about finding if the limit exists or not. So the L'Hospital's rule is not used in finding the limits.

When a function is examined at an input value, what are the possible deductions one can make about the function at that input value?

• Function is continuous
• Function is not continuous but defined
• Function is not continuous and not defined
• Any one of the above

The answer is 'Any one of the above'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Describing a function: A function f(x) is evaluated for three values to describe at an input value x=a

•  f(a)

•  lim_(x->a-) f(x)

•  lim_(x->a+) f(x)

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

If a function is not defined at an input value, can it be continuous at that input value?

• Yes. If the limits are equal.
• No. Irrespective of limits if the function is not defined at an input value, it is not continuous.

The answer is 'No. Irrespective of limits if the function is not defined at an input value, it is not continuous at that input value.'

Progress

Progress

A function f of x is examined at an input value x=a. Which of the following is to be examined?
f;a
f of a
left
left-hand-limit
right
right-hand-limit
all;above
all the above
The answer is 'all the above'.
It is important to note that the lopital rule is applicable only if the limit exists. The discussion in this topic is about finding if the limit exists or not. So the lopital rule is not used in finding the limits.
When a function is examined at an input value, what are the possible deductions one can make about the function at that input value?
continuous
Function is continuous
not
Function is not continuous but defined
defined
Function is not continuous and not defined
any;one;above
Any one of the above
The answer is 'Any one of the above'.
Whether a function is continuous or defined or not defined is determined by examining ;; value at the input value, left-hand-limit at the input value, and, right-hand-limit at the input value.
Describing a function: A function f of x is evalated for three values to describe at an input value x = q ;; f of a ;; limit x tending to a. minus, f of x ;; and limit x tending to a. +, f of x .
If a function is not defined at an input value, can it be continuous at that input value?
yes;s;equal
Yes. If the limits are equal.
no;irrespective;defined;not;defined
No. Irrespective of limits if the function is not defined at an input value, it is not continuous.
The answer is 'No. Irrespective of limits if the function is not defined at an input value, it is not continuous at that input value.'

we are not perfect yet...