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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

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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

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Change of Variable in a Limit

» variable can be substituted*when value is not any of the forms of `0/0`*

→ `lim_(x->a)f(x)` ` = lim_(y->g(a))f(g^(-1)(y))`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

The variable in a limit can be changed.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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Algebra of limit with change of variable is explained.

Starting on learning "Limit with change of variables". Algebra of limit with change of variable is explained.

Given

`lim_(x->0) (sin x)/x = 1` ;

What is `lim_(x->0) (sin(x^2))/x`?

- cannot find the limit
- take `y=x^2` and rearrange the function

The answer is 'take `y=x^2` and rearrange the function'

`lim_(x->0) (sin(x^2))/x`

`quad quad = lim_(x->0) x (sin(x^2))/(x^2)`

`quad quad = lim_(x->0) x xx lim_(y->0) (sin y)/y`

where `y=x^2` and `lim_(x->0)` changes to `lim_(y->0)` by the definition of y. `quad quad = 0 xx 1`

`quad quad = 0`

Note: If, in another case, `y=cos x` then `lim_(x->0)` changes to `lim_(y->1)`, as `y=cos 0 = 1`.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Change of variable in a Limit: ** Given that `y=g(x)` exists at `x=a`. Then

`lim_(x->a)f(x)`

`quad quad = lim_(y->g(a))f(g^(-1)(y))`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

*your progress details*

Progress

*About you*

Progress

given that limit x tending to 0, sine x by x = 1;; what is limit x tending to 0, sine x squared by x?

cannot;find

cannot find the limit

take;y;why;x;squared

take y = x squared and rearrange the function

The answer is "take y = x squared and rearrange the function" ;; limit x tending to 0, sine x squared by x ;; equals limit x tending to 0 x into sine x squared by x squared ;; equals limit x tending to 0 x into limit y tending to 0 sine y by y ;; where y equals x squared, and limit x tending to 0 changes to limit y tending to 0 by the definition of y. ;; equals 0 multiplied 1 ;; equals 0 ;; Note: If, in another case, y = cos x then limit x tending to 0 changes to limit y tending to 1 as y, = cos 0, = 1.

The variable in a limit can be changed.

Change of variable in a Limit: Given that y = g of x exists at x=a. Then limit x tending to a f of x, = limit y tending to, g of a, f of, g inverse, of y