# Solving Confusing Limits Homework

• BloodyFrozen
In summary, the problem involves finding the limit of two expressions: limh->0 (sqrt(a+h)-sqrt(a))/h and limx->1 (1-sqrt(x))/(1-x). The first expression can be solved using the conjugate method while the second one can be solved by factoring the numerator. Both solutions result in 1/2.
BloodyFrozen

## Homework Statement

1. limh->0 (sqrt(a+h)-sqrt(a))/h
2. limx->1 (1-sqrt(x))/(1-x)

## Homework Equations

---------------------------------------------

## The Attempt at a Solution

I tried conjugate, etc., but couldn't solve it without L'H's Rule.

Using the conjugate will work. What did you get when you tried that?

Thanks I got 1/(2)for one and 1/2 for number 2

Last edited:
For the second one, try factoring the numerator like so:

$$1 - x =\left(1 - \sqrt{x}\right)\left(1 + \sqrt{x}\right)$$

The solution should then become obvious.

EDIT: And for the first one, multiplying by the conjugate of the numerator is what you need to do.

Thanks guys, got them.

Ignore my comment above this.

## 1. What are limits in math?

Limits in math refer to the value that a function or sequence approaches as the input or independent variable approaches a certain value. It is used to describe the behavior of a function near a specific point.

## 2. How do I solve limits?

To solve a limit, you can use various techniques such as direct substitution, factoring, rationalization, or L'Hopital's rule. It is important to also check for any discontinuities or holes in the graph of the function before evaluating the limit.

## 3. What are the common types of limits?

The common types of limits include one-sided limits, infinite limits, and limits at infinity. One-sided limits are used when the function approaches a value from one direction only. Infinite limits occur when the function approaches positive or negative infinity. Limits at infinity refer to the behavior of the function as the input approaches positive or negative infinity.

## 4. Why are limits important?

Limits are important in math because they help us understand the behavior of a function near a specific point. They are also used in calculus to find derivatives and integrals, which are essential in many real-life applications such as physics, engineering, and economics.

## 5. How can I improve my skills in solving limits?

To improve your skills in solving limits, it is important to practice with a variety of problems and techniques. You can also seek help from a tutor or join a study group to discuss and solve problems together. Additionally, understanding the concepts behind limits and their applications can also help improve your skills.

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