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Limit Calculator With Steps

Enter the function and other values in the given input boxes. Hit the Calculate button to evaluate the limit with steps using limits calculator.

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Limit Solver

Limit calculator is used to evaluate the limit functions with respect to a specified variable. The variable could be x, y, or z. The limit calculator solves the limits with steps and shows you each phase of calculation.

Below, you will find the limits definition, how to calculate limits without using limit finder, formula of limits, and some examples to understand the limits.

What are limits?

The idea of a  limit of a function is vital to the study of calculus. It is used in describing some of the significant theories in calculus such as definite integral of a function, derivative of a function, and continuity.

The limit of a function  f(x) defines the behavior of the function near to a specific x value. It does not essentially provide the value of the function at x.

\( \lim_{x \to c} f(x) = L \)

It can be read as the limit of f of x as x approaches c equals L.

The limit solver above can evaluate both right-hand and left-hand limits.

Limits formulas – Limits rules

Below, we have provided laws of limits.

Notation of limit

\( \lim_{x \to c} f(x) = L \)

Left-Hand limit

Right-Hand limit

Limits of trigonometric functions

Limits of logs and exponential functions

Limits of the form 1 ∞

Limits of x^n

Checking if limit exists

To check if limit exists for f(x) at x = a, we check if,

Left hand limit = Right hand limit = f(a)

L'hospital's rule

Where,

f(a) = 0

g(a) = 0

Then,

Limits sum rule

Limits product rule

Limits quotient rule

Limits power rule

Constant rule of limits

Limit of a constant function is equal to a constant.

How to evaluate limits?

Limit evaluator is designed specifically for the purpose of limits evaluation. But, we will explain the manual method to evaluate limits. Below example illustrates the handbook method with steps.

Example:
Evluate:

\( \lim_{x \to 2} (x^3+2x^2-5x+2) \)

Solution:

Step 1: Write down the value.

\( \lim_{x \to 2} (x^3+2x^2-5x+2) \)

Step 2: Apply the limit function to each element.

\( \lim_{x \to 2} (x^3) + \lim_{x \to 2} (2x^2) - \lim_{x \to 2}(5x) + \lim_{x \to 2}(2) \)

Step 3: Take the coefficients out of the limit function.

\( \lim_{x \to 2} (x^3) + 2 \lim_{x \to 2} (x^2) - 5 \lim_{x \to 2}(x) + \lim_{x \to 2}(x) + 2 \)

Step 4: Apply the limit by placing \( x -> 2 \) in the equation.
\( = 1(2^3)+2(2^2)-5(2)+2 \)
\( = 8+8-10+2 \)
\( = 8 \)

so, \( \lim_{x \to 2} (x^3+2x^2-5x+2) = 8 \)

You can use the l'hopital's rule calculator above to verify the answer of any limit function.

Here is the graph plotted for the above function.