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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.

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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

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Limit of Functions with Indeterminate Value

» A function `f(x)` at `x=a` is

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

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

If a function does not have value in real numbers and the two limits are not equal then the *function is indeterminate* at that input value.

*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 an indeterminate function is discussed. The condition under which a function is indeterminate is illustrated with an example.

Starting on learning "limit of functions with indeterminate values". ;; With an example, calculation of limits for an indeterminate function is discussed. The condition under which a function is indeterminate is illustrated with an example.

Given function `f(x)=tan x`. what is `f(x)|_(x=pi/2)`?

- `+oo`
- `-oo`
- `0`

The answer is '`+oo`'

`f(pi/2)`

`quad quad = tan(pi/2)`

`quad quad = oo`

Given function `f(x)=tan x`.what is left-hand-limit `lim_(x->pi/2-)f(x)`?

- `+oo`
- `-oo`
- `0`

The answer is '`+oo`'

`lim_(x->pi/2-)f(x)`

`quad quad = f(pi/2-delta)`

`quad quad = tan(pi/2-delta)`

`quad quad = (sin(pi/2-delta))/(cos(pi/2-delta))`

`quad quad = (cos(delta))/(sin(delta))`

`quad quad = 1/0`

`quad quad = oo`

Given function `f(x)=tan x`.what is right-hand-limit `lim_(x->pi/2+)f(x)`?

- `+oo`
- `-oo`
- `0`

The answer is '`-oo`'

`lim_(x->pi/2+)f(x)`

`quad quad = f(pi/2+delta)`

`quad quad = tan(pi/2+delta)`

`quad quad = (sin(pi/2+delta))/(cos(pi/2+delta))`

`quad quad = (cos(delta))/(-sin(delta))`

`quad quad = -1/0`

`quad quad = -oo`

Given function `f(x)=tan x`.

• `f(pi/2)=oo`

• `lim_(x->pi/2-)f(x) = oo`

• `lim_(x->pi/2+)f(x) = -oo`

The function is not continuous and not defined at `x=pi/2`.

If the function evaluates to `+-oo` or `0/0` and the limits are not equal, then the function is not defined at that input value.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Function not Defined: **If `f(a) !in RR` and `lim_(x->a-)f(x)` `!=lim_(x->a+)f(x)` then the function is not defined at `x=a`.

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Examine the function `f(x) = 1/(x-3)` at `x=3`.

- Continuous
- defined
- not defined

The answer is 'Not defined'

*your progress details*

Progress

*About you*

Progress

Given function f of x = tan x. What is f of x at x = pi by 2?

plus

plus infinity

minus

minus infinity

0

0

The answer is "plus infinity" ;; f of pi by 2, equals tan pi by 2, equals infinity.

Given function f of x = tan x. What is left-hand-limit limit x tending to pi by 2 minus, f of x?

plus

plus infinity

minus

minus infinity

0

0

The answer is "plus infinity". ;; limit x tending to pi by 2 minus, f of x ;; equals f of pi by 2 minus delta ;; equals tan pi by 2 minus delta ;; equals sine pi by 2 minus delta divided by cos pi by 2 minus delta;; equals cos delta by sine delta ;; equals 1 by 0;; equals infinity

Given function f of x = tan x. What is right-hand-limit, limit x tending to pi by 2 +, f of x?

plus

plus infinity

minus

minus infinity

0

0

The answer is "minus infinity". ;; limit x tending to pi by 2 +, f of x ;; equals f of pi by 2 + delta ;; equals tan pi by 2 + delta ;; equals sine pi by 2 + delta divided by cos pi by 2 + delta;; equals cos delta by minus sine delta ;; equals minus 1 by 0;; equals minus infinity

Given function f of x = tan x. ;; f of pi by 2 = infinity ;; limit x tending to pi by 2 minus, f of x = infinity;; limit x tending to pi by 2 +, f of x = minus infinity ;; the function is not continuous and not defined at x = pi by 2.

If the function evaluates to plus or minus infinity or 0 by 0 and the limts are not equal, then the function is not defined at that input value.

If a function does not have value in real numbers and the two limits are not equal then the function is indeterminate at that input value.

function not defined: if f of a not in rel numbers, and limit x tending to a. minus f of x not equals limit x tending to a. plus f of x, then the function is not defined at x = a.

Examine the function f of x equals 1 by x minus 3 at x=3.

continuous

Continuous

defined

defined

not defined;not

not defined

The answer is "not defined"