Basic limit question (limit of h as h approach 0)

In summary, a basic limit question is a type of mathematical question that involves finding the limit of a variable as it approaches a certain value, usually 0. To solve it, you need to plug in the value and simplify the function. The significance of h approaching 0 is that it represents the behavior of the function near a specific point. A basic limit question can have more than one possible answer, depending on the function and the approach used. These types of questions have practical applications in fields such as physics, engineering, and economics.
  • #1
Moogie
168
1
Hi

Why is the lim(h->0) of h = 0?

I'm new to this so I'm probably being thrown by the change in variable? Is it because we assume f is a function of h, f(h) = h which we know is continuous from other proofs elsewhere, which gives

lim(h->0) f(h) = f(0)
lim(h->0) h = 0

thanks
 
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  • #2
That's exactly right. And you'll go far in mathematics with such a healthily skeptical outlook!
 

1. What is a basic limit question?

A basic limit question is a type of mathematical question that involves finding the limit of a variable as it approaches a certain value, usually 0. It is commonly used in calculus to understand the behavior of functions near a specific point.

2. How do I solve a basic limit question?

To solve a basic limit question, you need to first plug in the value that the variable is approaching (in this case, 0) into the function. Then, simplify the function as much as possible and see if you can find a finite value. If not, you may need to use more advanced techniques such as L'Hopital's rule or graphing to find the limit.

3. What is the significance of h approaching 0 in a basic limit question?

In a basic limit question, h approaching 0 is significant because it represents the behavior of the function as it gets closer and closer to a specific point. This allows us to understand the behavior of the function near that point, which can be useful in many applications.

4. Can a basic limit question have more than one possible answer?

Yes, a basic limit question can have more than one possible answer. Depending on the function and the value that the variable is approaching, there may be different methods or approaches to solving the limit, which can result in different answers. It is important to carefully consider the context and the assumptions made when solving a basic limit question.

5. How can I apply basic limit questions in real life?

Basic limit questions have many practical applications in fields such as physics, engineering, and economics. For example, they can be used to understand the behavior of a system as it approaches a certain state or to calculate the rate of change of a variable. Understanding basic limit questions can also help in making predictions and analyzing data in various real-world situations.

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