# Solve Infinite Limit Problems: 2-x/(x-1)^2 & e^x/(x-5)^3

• montana111
In summary: If you meant e^x/(x - 5)^3, then you can use L'Hopital's rule to evaluate the limit.In summary, the book is asking to find the infinite limit for the function 2-x/(x-1)^2. The answer is infinity as the function grows large without bound as x approaches 1. The second problem may have a typo, but if it is e^x/(x-5)^3, L'Hopital's rule can be used to evaluate the limit.
montana111

## Homework Statement

the book says "find the infinite limit", but it says "lim as x --> 1 of 2-x/(x-1)^2
I don't understand this or how to find the answer. if it was an infinite limit, shouldn't it say as x approaches infinity? The back of my text says the answer is infinity but i don't know how to do the problem still. please help. I am expecting this stuff to be on my quiz this week

## Homework Equations

lim as x --> 1 of 2-x/(x-1)^2

and

lim as x --> -3^- of e^x/(x-5)^3

## The Attempt at a Solution

i started to make up numbers and factor our things but nothing worked. i got -1/1 from that for the first problem. i have no idea for the second one.

"infinite limit" sounds like an oxymoron to me.

Why don't you try plugging some numbers into the first example such as .9, .99, .999 or 1.1, 1.01, 1.001. Do you see f(x) approaching a limit?

For your first problem, as x approaches 1 from either side, the numerator approaches 1 (I'm assuming you meant (2 - x)/(x - 1)^2 but left off parentheses in the numerator), and the denominator approaches 0. As a result, the function grows large without bound.

A "limit at infinity" is one where the variable approaches infinity or negative infinity, and the resulting limit can be finite, infinte, or not exist.

For your second problem, is there a typo? As you have written it, the limit can be obtained by evaluating the function at -3.

## 1. What is an infinite limit problem?

An infinite limit problem is a mathematical concept that involves finding the behavior of a function as the input variable approaches infinity or negative infinity. It is used to determine the value of a function at a point where the function is undefined or when the limit does not exist.

## 2. How do I solve an infinite limit problem?

To solve an infinite limit problem, you need to follow a step-by-step process. First, simplify the expression by factoring and canceling common terms. Then, check the degree of the numerator and denominator to determine the type of limit (finite or infinite). Finally, use algebraic manipulation or L'Hopital's rule to evaluate the limit.

## 3. What are some common types of infinite limit problems?

Some common types of infinite limit problems include rational functions with a polynomial in the denominator, exponential functions with a polynomial in the exponent, and trigonometric functions with a variable in the argument. These types of problems require different approaches to solve them.

## 4. What is the difference between a finite and an infinite limit?

A finite limit is a value that the function approaches as the input variable gets closer to a particular point. It means that the function is defined and continuous at that point. In contrast, an infinite limit is a value that the function approaches as the input variable gets closer to a particular point, but the function is undefined or discontinuous at that point.

## 5. How can I use limits to evaluate the behavior of a function?

Limits can help us understand the behavior of a function by determining the values that the function approaches as the input variable gets closer to a particular point. They can also help us identify whether a function is continuous or discontinuous at a specific point. Additionally, limits can be used to find the derivative of a function, which is essential in many applications in mathematics and science.

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