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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

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Limit of a Function

» If both left-hand-limit and right-hand-limit are equal, it is together referred as "limit of the function"

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

When left-hand-limit and right-hand-limit are equal, the limits are referred together as *limit of a function*.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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The right-hand and left-hand limits are equal for most input values for most functions. This is commonly referred as limit of a function.

Starting on learning "limit of a function". ;; The right-hand and left-hand limits are equal for most input values for most functions. This is commonly referred as limit of a function.

Given that function `f(x)` evaluates to indeterminate value at `x=a`. To evaluate the expected value of `f(x)|_(x=a)`, we examine ;

• Left-hand-limit `lim_(x->a-) f(x)`

• Right-hand-limit `lim_(x->a+) f(x)`

If these two limits are equal then the result is referred as "*limit of the function at the input value*" `lim_(x->a) f(x)`

The significance of this is that, most functions have both right-hand-limit and left-hand-limit equal.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

** Limit of a function: ** Given function `f(x)` and that `f(x)|_(x=a) = 0/0`.

If `lim_(x->a+) f(x) = lim_(x->a-) f(x)`,

then the common value is referred as limit of the function `lim_(x->a) f(x)`.

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

If a function `f(x)` is discontinuous at `x=a`, then what is `lim_(x->a) f(x)`?

- left-hand-limit
- right-hand-limit
- `f(a)`
- cannot be computed

The answer is 'cannot be computed'. It is given that the function is discontinuous at `x=a`, and that implies left-hand-limit and right-hand-limits are not equal. In that case, limit of the function cannot be computed without specifying left or right.

*your progress details*

Progress

*About you*

Progress

Given that function f of x evaluates to indeterminate value at x=a. To evaluate the expected value of f of x at x=a, we examine ;; Left-hand-limit limit x tending to a. minus f of x ;; Right-hand-limit limit x tending to a. plus f of x ;; If these two limits are equal then the result is referred as "limit of the function at the input value" limit x tending to a. f of x ;; The significance of this is that, most functions have both right-hand-limit and left-hand-limit equal.

When left-hand-limit and right-hand-limit are equal, the limits are referred together as limit of a function

Limit of a function: Given function f of x and that f of x at x=a equals 0 by 0.;; If limit x tending to a. plus f of x equals limit x tending to a. minus f of x ;; then the common value is referred as limit of the function limit x tending to a. f of x.

If a function f of x is discontinuous at x=a, then what is limit x tending to a. f of x?

left

left-hand-limit

right

right-hand-limit

f;a

f of a

cannot;computed

cannot be computed

The answer is 'cannot be computed'. It is given that the function is discontinuous at x=a , and that implies left-hand-limit and right-hand-limits are not equal. In that case, limit of the function cannot be computed without specifying left or right.