How to Calculate Limit of N-1 N 1

What is a Limit in Calculus?

A limit is a fundamental concept in calculus that describes the value that a function approaches as the input approaches a certain value. Limits are used to define continuity, derivatives, and integrals. In this case, we're calculating the limit of the function (n-1)/n as n approaches 1.

Understanding limits is crucial for solving more complex calculus problems and has applications in physics, engineering, economics, and other fields.

Limit Formula

The general formula for a limit is:

For our specific problem, the function is (n-1)/n and we're interested in the limit as n approaches 1.

How to Calculate the Limit

Calculating the limit of (n-1)/n as n approaches 1 involves direct substitution. Here's the step-by-step process:

1. Identify the function: f(n) = (n-1)/n
2. Substitute the value that n is approaching (1) into the function: f(1) = (1-1)/1 = 0/1 = 0
3. Since the function is defined at n=1 and the limit equals the function value, the limit is 0.

Worked Example

Let's calculate the limit of (n-1)/n as n approaches 1 using the calculator provided in the sidebar.

1. Enter n = 1 in the calculator.

2. Click "Calculate".

The calculator will show that the limit is 0, which matches our manual calculation.

This example demonstrates how to apply the limit concept to a simple function.