Calculator for limits (of functions, one variable)

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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: