Limits Calculator

Use * to indicate multiplication between coefficients and variables. For example, enter 3*x^3+2*x^2, instead of 3x^3+2x^2.



Solution:

Examples:

  • To solve \(\lim\limits_{x\to 0}\frac{2x^2+1}{x+1}\), enter (2*x^2+1)/(x+1), the variable x and the limit 0.
  • To solve \(\lim\limits_{x\to 0}\frac{x^2+2x-3}{x^6+4}\), enter (x^2+2*x-3)/(x^6+4), the variable x and the limit 0.
  • To solve \(\lim\limits_{t\to 2}t^t-1\), enter t^t-1, the variable t and the limit 2.

With this calculator, you can find the limit of an expression as it approaches a certain value. You must enter the expression, specify the variable, and enter the limit to evaluate.

How to use the limit calculator?

Step 1: Enter the algebraic expression in the first input box. You must use * to indicate multiplication between variables and coefficients. This means that instead of entering 2x or 4x^2, you must enter 2*x or 4*x^2.

Step 2: Enter the main variable in the second input box. In most cases, the variable is x.

Step 3: Enter the limit for which to evaluate in the third input box.

Step 4: Click “Solve” to find the limit of the input data.

Step 5: The solution along with the entered limit will be displayed at the bottom.

How to enter expressions in the limit calculator?

To enter expressions, we must consider some important aspects. First, we have to use * to indicate multiplication between coefficients and variables. For example, 4x or 2x^3 should be entered as 4*x or 2*x^3 respectively.

Also, to enter exponents, we must use the ^ sign. For example, we can write x^2 or x^3 to indicate that we are squaring and cubing, respectively.

We can use parentheses and the / sign to enter rational expressions. Using parentheses helps us correctly indicate that an entire expression is in the denominator.

The following are some examples of how we should enter expressions in the calculator:

  • To solve \(\lim\limits_{x\to 0}\frac{x^2+2}{x+3}\), enter (*x^2+2)/(x+3), the variable x and the limit 0.
  • To solve \(\lim\limits_{x\to 5}\frac{3x^2+x-1}{x^3+4}\), enter (3*x^2+x-1)/(x^3+4), the variable x and the limit 0.
  • To solve \(\lim\limits_{t\to 2}t^t-1\), enter t^t-1, the variable t and the limit 2.

What are limits?

Limits are the values to which the output values of function approach as the input values approach a certain value. Limits are essential in calculus and mathematical analysis and are used to define the continuity of functions, derivatives, and integrals.

How to solve limits manually?

One of the easiest methods of solving limits is simply to evaluate the expression within the limit for the given value. For example, if we have the limit \(\lim\limits_{x\to 0}\frac{x^2+2}{x+3}\), we can substitute the value of x=0 into the expression \(\frac{x^2+2}{x+3}\).

Doing this, we get \(\frac{2}{3}\). However, this will only be useful for limits that are not undefined, so this method is very limited.

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