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Math Calculators ▶ Limit Calculator

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**Table of Content**

Evaluate the positive and negative limits of a given function at any point with this advanced limit calculator. With that, the limit solver functions to provide complete steps required to resolve a given function limit.

Also, this l’hopital’s rule calculator helps to calculate \(\frac{0}{0}\) and \(\frac{\infty}{\infty}\) limit problems and supports computing limits at positive and negative infinities.

It can be defined as:

**“The behavior of a function at a certain point for any input change”**

Limit notation represents a mathematical concept that is based on the idea of closeness. It is necessary to evaluate the limit in calculus either by calculus limit calculator or by hand.

The limit definition calculator assigns values to certain functions at points where no values are defined. It does this all in such a way as to be consistent with proximate or near values.

This best lim calculator with steps works by analyzing various limit operations. These laws can be used to assess the limit of a polynomial or rational function.

Additionally, there are certain conditions for some rules and if they are not satisfied, then the rule cannot be used to validate the evaluation of a limit. However, using a limit evaluator is the best way to evaluate the limits of a function at any point.

The following table summarises the limit laws along with some central properties:

Rules |
Expressions |

Sum/Difference Rule | lim[f(x) ± h(x)] = lim_{x→b}[f(x)] ± lim_{x→b}[h(x)]_{x→b} |

Power Rule | lim[f(x)_{x→b}^{n}] = [lim[f(x)]]_{x→b}^{n} |

Product Rule | lim[f(x) * h(x)] = lim_{x→b}[f(x)] * lim_{x→b}[h(x)]_{x→b} |

Constant Rule | lim[k] = k_{x→b} |

Quotient Rule | lim[f(x) / h(x)] = lim_{x→b}[f(x)] / lim_{x→b}[h(x)]_{x→b} |

L’Hopital’s Rule | lim[f(x) / h(x)] = lim_{x→b}[f'(x) /h'(x)]_{x→b} |

What about resolving a few examples to comprehend how you make use of the various methods to simplify limits?

Evaluate the limit of the function below:

\(\lim_{x \to 3} 4x^{3}+6x{2}-x+3\)

Here we will be using the substitution method:

**Step 01:**

Apply a limit to each and every value in the given function separately to simplify the solution:

\(= \lim_{x \to 3} \left(4x^{3}\right)+\lim_{x \to 3} \left(6x^{2}\right) – \lim_{x \to 3} \left(x\right) + \lim_{x \to 3} \left(3\right)\)

**Step 02:**

Now write down each coefficient as a multiple of the separate limit functions:

\(= 4 * \lim_{x \to 3} \left(x^{3}\right)+6 * \lim_{x \to 3} \left(x^{2}\right) – \lim_{x \to 3} \left(x\right) + \lim_{x \to 3} \left(3\right)\)

**Step 03:**

Substitute the given limit i.e; \(\lim_{x \to 3}\):

\(\lim_{x \to 3} 4x^{3}+6x{2}-x+3 = 4 * \left(3^{3}\right) + 6 * \left(3^{2}\right) – 3 + 3\)

**Step 04:**

Simplify to get the final answer:

\(\lim_{x \to 3} 4x^{3}+6x{2}-x+3 = 4 * 27 + 6 * 9 – 3 + 3\)

\(\lim_{x \to 3} 4x^{3}+6x{2}-x+3 = 108 + 6 * 9 – 3 + 3\)

\(\lim_{x \to 3} 4x^{3}+6x{2}-x+3 = 162\)

This is the required answer that can also be checked with a limit calculator with steps.

How to do limits for the function given as below:

$$ \lim_{x \to 0} \left(\frac{sin x}{x}\right) $$

Using the substitution method:

\(\lim_{x \to 0} \left(\frac{sin x}{x}\right)\)

\(= \frac{sin 0}{0}\)

\(= \frac{0}{0}\)

Which is an indeterminate form. So here we will be applying l’hopital’s rule:

Before we move on, we have to check whether both the functions above and below the vinculum are differentiable or not.

\(\frac{d}{dx} \left(sin x\right) = cos x\)

\(\frac{d}{dx} \left(x\right) = 1\)

Moving ahead further now:

\(\lim_{x \to 0} \left(\frac{cos x}{1}\right)\)

\(= \frac{cos 0}{1}\)

\(= 1\)

To speed up your calculations, try using the l’Hospital rule calculator.

Our limit finder is straightforward to use! It requires a few inputs to calculate limits of the given function at any point that include:

**Input:**

- First of all, enter the equation or function.
- Select the variable from the drop-down with respect to which you need to evaluate the limit. It can be x,y,z,a,b,c, or n.
- Specify the number at which you want to calculate the limit. In this field, you can use a simple expression as well such as inf=∞ or pi =π.
- Now select the direction of the limit. It can be either positive or negative
- Once you enter the values in the given fields, the calculator will give you an equation preview.
- Hit the calculate button.

**Output:**

- Limits of the given function
- Step by step calculations
- Taylor’s series expansion for the given function

From the authorized source of Wikipedia: Limit (mathematics), function, sequence, standard parts and much more!

The source of Khan Academy provides with: Best Strategy in finding limits

Other Languages: Limit Hesaplama, Kalkulator Limit, Grenzwertrechner, Kalkulačka Limit, Calculadora De Limites, Calculateur De Limite, Calculadora De Limites, Calcolatore Limiti, Калькулятор Пределов.