To calculate result you have to disable your ad blocker first.

# Limit Calculator

Enter the function & limit in the fields below, select the variable, and hit **submit **button to solve the limit using limits calculator.

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

* *

Table of Contents:

## Limit Calculator with steps

Limit calculator is an online tool that evaluates limits for the given functions and shows all steps. It solves limits with respect to a variable. Limits can be evaluated on either left or right hand side using this limit solver.

## What are Limits?

**“**The limit of a function is the value that ** f(x)** gets closer to as

**approaches some number.**

*x***”**

**Lim _{x→b} [f(x)] = L**

Limits are vital to mathematical analysis and calculus. They are also used to define derivatives, integrals, and continuity.

## Rules of Limits

Here are some well-known rules/laws/properties of limits.

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} |

## How to evaluate Limits?

Using the online limit calculator is the best way to solve limits, however, we will discuss the manual method to evaluate limits. Follow the below example to understand step by step method to solve limits.

*Example:*

Find the limit:

`Iim`

_{x→2}(x^{3 }+ 4x^{2 }− 2x + 1)

**Solution:**

**Step 1: **Apply the **limit function** separately to each value.

= Iim** _{x→2}**(x

^{3}) + Iim

**(4x**

_{x→2}^{2}) - Iim

**(2x) + lIim**

_{x→2}**(1)**

_{x→2}**Step 2: **Separate **coefficients **and get them out of the limit function.

= Iim** _{x→2}**(x

^{3}) + 4 Iim

**(x**

_{x→2}^{2}) - 2 Iim

**(x) + Iim**

_{x→2}**(1)**

_{x→2}**Step 3: **Apply the limit value by substituting ** x = 2 **in the equation to find the limit.

Iim** _{x→2}**(x

^{3 }+ 4x

^{2 }− 2x + 1)

*= 1(2*

^{3}) + 4(2^{2}) – 2(2) + 1Iim** _{x→2}**(x

^{3 }+ 4x

^{2 }− 2x + 1)

*= 8 + 16 – 4 + 1*

**Iim _{x→2}(x^{3 }+ 4x^{2 }− 2x + 1) = 21**

The limit finder above also uses L'hopital's rule to solve limits.

You can also use our L'hopital's rule calculator to solve the Limits for undefined functions (**0/0**, **∞/∞**).

## References

- Wikimedia Foundation. What are Limits? Wikipedia.
- OpenStaxCollege. (2016, February 1). Rules of Limits. 2.3 The Limit Laws | Calculus Volume 1.