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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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Limit of Polynomials

*Apply Algebra of Limits* For a function `f(x) = a_nx^n``+a_(n-1)x^(n-1)``+ cdots ``+ a_1x^1 ``+ a_0`

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

`quad quad = a_n lim_(x->a) x^n``+a_(n-1) lim_(x->a) x^(n-1)``+ cdots ``+ a_1 lim_(x->a) x^1 ``+ a_0`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

Limit of a polynomial is the limit on individual terms of the polynomial.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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Finding limit of standard polynomial expressions is explained with an example.

Starting on learning "limit of polynomials". ;; Finding limit of standard polynomial expressions is explained with an example.

How to find limits of function `f(x)=3x^3+2x^2-1` at `x=-2`

- apply limit to the three terms of the function
- one has to memorize a formula

The answer is 'apply limit to the three terms of the function'

limit of function `f(x)=color(deepskyblue)(3x^3)+color(coral)(2x^2)-1` at `x=-2`

By Substitution :

`f(x)|_(x=-2)`

`quad quad = color(deepskyblue)(3(-2)^3)+color(coral)(2(-2)^2)-1`

`quad quad = color(deepskyblue)(3(-8))+color(coral)(2(4))-1`

`quad quad = -17`

limits of function `f(x)=color(deepskyblue)(3x^3)+color(coral)(2x^2)-1` at `x=-2`

left-hand-limit :

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

`quad quad = color(deepskyblue)(3(-2-delta)^3)+color(coral)(2(-2-delta)^2)-1`

substitute `delta=0`

`quad quad = color(deepskyblue)(3(-8))+color(coral)(2(4))-1`

`quad quad = -17`

limits of function `f(x)=color(deepskyblue)(3x^3)+color(coral)(2x^2)-1` at `x=-2`

right-hand-limit :

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

`quad quad = color(deepskyblue)(3(-2+delta)^3)+color(coral)(2(-2+delta)^2)-1`

substitute `delta=0`

`quad quad = color(deepskyblue)(3(-8))+color(coral)(2(4))-1`

`quad quad = -17`

limits of function `f(x)=3x^3+2x^2-1` at `x=-2`

`f(x)|_(x=-2) = -17`

`lim_(x->-2-)f(x)= -17`

`lim_(x->-2+)f(x)= -17`

All three values are equal. So the function is continuous.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Limit of a polynomial: ** For a function `f(x) = a_nx^n+a_(n-1)x^(n-1)+ cdots + a_1x^1 + a_0`

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

`quad quad = a_n lim_(x->a) x^n+a_(n-1) lim_(x->a) x^(n-1)+ cdots `

`quad quad quad quad + a_1 lim_(x->a) x^1 + a_0`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

*your progress details*

Progress

*About you*

Progress

How to find limits of function f of x equals 3 x cube + 2 x squared minus 1 at x = minus 2 ?

apply;limit;3;terms

apply limit to the three terms of the function

one;has;memorize;

one has to memorize a formula

The answer is 'apply limit to the three terms of the function'

limits of function f of x = 3 x cube + 2 x squared minus 1 at x = minus 2 ;; by substitution : f of x at x equal minus 2;; equals 3 into minus 2 cubed + 2 into minus 2 squared minus 1;; equals 3 into minus 8 + 2 into 4 minus 1;; equals minus 17.

limits of function f of x = 3 x cube + 2 x squared minus 1 at x = minus 2 ;; left hand limit equals 3 into minus 2 minus delta cubed + 2 into minus 2 minus delta squared minus 1;; substitute delta = 0;; equals 3 into minus 8 + 2 into 4 minus 1;; equals minus 17.

limits of function f of x = 3 x cube + 2 x squared minus 1 at x = minus 2 ;; right hand limit equals 3 into minus 2 plus delta cubed + 2 into minus 2 plus delta squared minus 1;; substitute delta = 0;; equals 3 into minus 8 + 2 into 4 minus 1;; equals minus 17.

Limits of function f of x = 3 x cube + 2 x squared minus 1 at x = minus 2;; f of x at x = minus 2, = minus 17;; limit x tending to minus 2 minus, f of x = minus 17;; limit x tending to minus 2 plus, f of x = minus 17;; All the three values are equal. So the function is continuous.

Limit of a polynomial is the limit on individual terms of the polynomial.

Limit of a polynomial is the limit on individual terms of the polynomial. This is given in mathematical form.