# Limiting x^2/(x-1) as x Approaches 1 from the Left

• DrummingAtom
In summary, the limit of x^2/(x-1) as x goes to 1 from the left is negative infinity. This can be shown algebraically by factoring the numerator and using the limit rules for fractions.
DrummingAtom

## Homework Statement

Find the limit of x^2/(x-1) as x goes to 1 from the left.

## The Attempt at a Solution

It doesn't seem I can factor anything, but could I assume that since the numerator is a constant and the denomination is going to be negative because it's <1 then it's going to negative infinity? Is there anyway to show this algebraically? Thanks.

DrummingAtom said:

## Homework Statement

Find the limit of x^2/(x-1) as x goes to 1 from the left.

## The Attempt at a Solution

It doesn't seem I can factor anything, but could I assume that since the numerator is a constant and the denomination is going to be negative because it's <1 then it's going to negative infinity? Is there anyway to show this algebraically? Thanks.

You are correct.

$$\frac{x^2}{1-x} = \frac{x^2 -1}{1-x} + \frac{1}{1-x}$$

The limit as x-> $$1^{-}$$ of $$\frac{x^2 -1}{1-x}$$ is 2.
This
$$\frac{1}{1-x}$$ one does not exist.

## What is the limit of x^2/(x-1) as x approaches 1 from the left?

The limit of x^2/(x-1) as x approaches 1 from the left is undefined. This is because when x approaches 1 from the left, the denominator (x-1) becomes very close to 0, which would result in division by 0.

## Why is the limit of x^2/(x-1) as x approaches 1 from the left undefined?

The limit of x^2/(x-1) as x approaches 1 from the left is undefined because the denominator (x-1) becomes very close to 0, which would result in division by 0. In mathematics, division by 0 is undefined.

## What happens to the value of x^2/(x-1) as x gets closer and closer to 1 from the left?

As x gets closer and closer to 1 from the left, the value of x^2/(x-1) becomes larger and larger. This is because as x approaches 1, the denominator (x-1) becomes smaller and smaller, making the fraction larger.

## Can the limit of x^2/(x-1) as x approaches 1 from the left be calculated using direct substitution?

No, the limit of x^2/(x-1) as x approaches 1 from the left cannot be calculated using direct substitution. Direct substitution would result in division by 0, which is undefined.

## How can the limit of x^2/(x-1) as x approaches 1 from the left be calculated?

The limit of x^2/(x-1) as x approaches 1 from the left can be calculated using the concept of one-sided limits. This involves evaluating the limit as x approaches 1 from values slightly less than 1, such as 0.9, 0.99, 0.999, and so on. If the values from the left side approach a specific number, then that number is the limit from the left. However, in this case, the limit from the left does not exist as the values get closer and closer to 1, the limit also gets larger and larger, approaching infinity.

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