Understanding the Limit as x Approaches 1 from the Right Side in Mathematics

lim x–>1+

In mathematics, the notation “lim x–>1+” represents the limit as x approaches 1 from the right side

In mathematics, the notation “lim x–>1+” represents the limit as x approaches 1 from the right side. This means that x is getting closer and closer to 1, but always remaining greater than 1.

To find the limit as x approaches 1 from the right side, we analyze the behavior of the function as x gets closer and closer to 1, but remains greater than 1.

Here’s an example to illustrate this concept:

Let’s consider the function f(x) = 1/(x – 1). We want to find the limit as x approaches 1 from the right side.

When x gets very close to 1, but is still greater than 1, the function f(x) becomes very large in magnitude. As x approaches 1, the denominator (x – 1) gets closer and closer to 0, resulting in a very large value for the function.

We can see this by plugging in values of x that are very close to 1, but greater than 1:

f(1.1) = 1/(1.1 – 1) = 1/0.1 = 10
f(1.01) = 1/(1.01 – 1) = 1/0.01 = 100
f(1.001) = 1/(1.001 – 1) = 1/0.001 = 1000

As x gets closer and closer to 1, the function f(x) grows larger and larger in magnitude. The limit as x approaches 1 from the right side is said to be infinity, which can be represented as lim x–>1+ f(x) = ∞.

In summary, the limit as x approaches 1 from the right side means analyzing the behavior of a function as x gets very close to 1, but always remaining greater than 1. It involves determining whether the function approaches a particular value, such as a number, infinity, or negative infinity.

More Answers: