Limit Problem: Solving \lim_{x \to 2} \frac{\tan (2 - \sqrt{2x})}{x^2 - 2x}

Thread starter gede
Start date Feb 28, 2016
Tags

Limit

In summary: The next step would be to factor the denominator as ##(x-1)(x^2+x+1)## and then use the fact that ##\lim_{x \to 1} \frac{1-x}{x-1} = -1## and ##\lim_{x \to 1} \frac{x^2+x+1}{x-1} = 3## to simplify the limit.

Mar 4, 2016

Ssnow

Gold Member

Mark44 said:

In English these are called indeterminate forms.

Yes sorry, an error in the translation ...

<h2>What is a limit problem?</h2><p>A limit problem is a mathematical concept that involves finding the value that a function approaches as its input approaches a certain value. In other words, it is the value that the function "approaches" or gets closer to, but may not necessarily reach, as the input gets closer to a specific value.</p><h2>What does the notation \lim_{x \to a} f(x) represent?</h2><p>The notation \lim_{x \to a} f(x) represents the limit of the function f(x) as x approaches the value a. This means that we are interested in the behavior of the function as the input gets closer and closer to the value a.</p><h2>How do you solve a limit problem?</h2><p>To solve a limit problem, you can use various methods such as algebraic manipulation, substitution, and graphing. In some cases, you may also need to use special limit theorems or techniques, such as L'Hopital's rule, to evaluate the limit.</p><h2>What is the limit of the given function \lim_{x \to 2} \frac{\tan (2 - \sqrt{2x})}{x^2 - 2x}?</h2><p>The limit of the given function is undefined or does not exist. This is because when x approaches 2, the denominator of the function becomes 0, which is undefined. Therefore, the function does not have a well-defined limit at x = 2.</p><h2>Why is it important to solve limit problems?</h2><p>Solving limit problems is important in mathematics because it helps us understand the behavior of a function near a specific value. It also allows us to make predictions and draw conclusions about the behavior of a function without actually evaluating it at that specific value. In addition, limits are essential in calculus and other areas of mathematics, making it a fundamental concept to understand.</p>

What is a limit problem?

A limit problem is a mathematical concept that involves finding the value that a function approaches as its input approaches a certain value. In other words, it is the value that the function "approaches" or gets closer to, but may not necessarily reach, as the input gets closer to a specific value.

What does the notation \lim_{x \to a} f(x) represent?

The notation \lim_{x \to a} f(x) represents the limit of the function f(x) as x approaches the value a. This means that we are interested in the behavior of the function as the input gets closer and closer to the value a.

How do you solve a limit problem?

To solve a limit problem, you can use various methods such as algebraic manipulation, substitution, and graphing. In some cases, you may also need to use special limit theorems or techniques, such as L'Hopital's rule, to evaluate the limit.

What is the limit of the given function \lim_{x \to 2} \frac{\tan (2 - \sqrt{2x})}{x^2 - 2x}?

The limit of the given function is undefined or does not exist. This is because when x approaches 2, the denominator of the function becomes 0, which is undefined. Therefore, the function does not have a well-defined limit at x = 2.

Why is it important to solve limit problems?

Solving limit problems is important in mathematics because it helps us understand the behavior of a function near a specific value. It also allows us to make predictions and draw conclusions about the behavior of a function without actually evaluating it at that specific value. In addition, limits are essential in calculus and other areas of mathematics, making it a fundamental concept to understand.