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Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

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

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

Welcome to **nub****trek**.

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

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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.

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

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

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

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

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`

*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

You are learning the free content, however do shake hands with a coffee to show appreciation.

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

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.'

*your progress details*

Progress

*About you*

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.'