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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

Limit of Function with abrupt change

» A function `f(x)` at `x=a` is

→ **continuous**: if `f(a)` = LHL = RHL

*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

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

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

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

The answer is 'continuous'

*your progress details*

Progress

*About you*

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

The answer is "0"

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

The answer is "0"

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

The answer is "0"

Given function f of x = mod x minus 1. ;; f of 1 equal 0;; limit x tending to 1 minus, f of x = 0;; limit x tending to 1 +, f of x = 0 ;; The function is continuous at x=1. ;; Note that the function undergoes an abrupt change at x =1. For x less than 1, the slope of the line is minus 1;; for x greater than 1, the slope of the line is +1;; at x=1 the slope of the line is not defined.

Given the function f of x = mod sine x. Is the function continuous or defined at x=pi?

continuous

continuous

defined

defined and not continuous

not defined

not defined and not continuous

The answer is "continuous"