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Limit of Algebraic Expressions

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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

Limit of Polynomials

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.

Keep tapping on the content to continue learning.
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

Progress

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.

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