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Calculator for limits (of functions, one variable)

Krystian Karczyński

Founder and General Manager of eTrapez.

Graduate of Mathematics at Poznan University of Technology. Mathematics tutor with many years of experience. Creator of the first eTrapez Courses, which have gained immense popularity among students nationwide.

He lives in Szczecin, Poland. He enjoys walks in the woods, beaches and kayaking.


I present another calculator, this time for functions of one variable:

The principle – simple as ever. In the field “f(x) =” we enter the function/expression from which we want to compute the limit, according to the general rules for entering mathematical formulas.

In the field “x – >” we enter what x is aiming at.

We click on “Calculate.”

Note 1 – how to type infinity \infty ?

Infinity type:

  • or by typing the lowercase o twice, ie: “oo”
  • Or, for example, by typing the word “infinity”
Note 2 – how to write below or above limits?
  • x \to {{0} ^{+}} we type “0+”
  • x \to {{2} ^ {-}} type "2-"

Example 1

I want to count the boundary of the function \underset{x\to 1}{\mathop{\lim }}\,\frac{x-1}{{{x}^{2}}-1}.

I type in the field “f(x)=”:  (x-1) /(x^2-1)

I type in the “x – >” field: 1

I click on “Calculate.”

I got the result: \underset{x\to 1}{\mathop{\lim }}\,\frac{x-1}{{{x}^{2}}-1}=\frac{1}{2}

Example 2

I want to count the limit of the function \underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{7}}+5{{x}^{5}}-4{{x}^{3}}+2x-1}{10{{x}^{7}}+{{x}^{6}}+{{x}^{5}}+{{x}^{4}}+{{x}^{3}}+{{x}^{2}}+x+1}

I type in the field “f(x)=”: (x^7+5x^5-4x^3+2x-1)/(10x^7+x^6+x^5+x^4+x^3+x^2+x+1)

I type in the “x – >” field: oo

Or:

I type in the field “x – >”: infinity

I click on “Calculate.”

I got the result: \underset{x\to \infty }{\mathop{\lim }}\,\frac{{{x}^{7}}+5{{x}^{5}}-4{{x}^{3}}+2x-1}{10{{x}^{7}}+{{x}^{6}}+{{x}^{5}}+{{x}^{4}}+{{x}^{3}}+{{x}^{2}}+x+1}=\frac{1}{10}

Example 3

I count the limit of the function \underset{x\to {{0}^{+}}}{\mathop{\lim }}\,{{e}^{\frac{1}{x}}}\left( {{\cos }^{2}}x-1 \right)

I type in “f(x)=”: e^(1/x)((cosx)^2-1)

I type in the “x – >” field: 0+

I click on “Calculate.”

I got the result: \underset{x\to {{0}^{+}}}{\mathop{\lim }}\,{{e}^{\frac{1}{x}}}\left( {{\cos }^{2}}x-1 \right)=-\infty

Video Manual

A brief discussion of the calculator also in this video:

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