Solving Simple Limits with Examples

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In summary, the conversation is about finding the limit of the function (f(x + delta x) - f(x)) / delta x as delta x approaches 0, where f(x) = 2x + 3. The participants discuss how to properly write the problem and how to handle the function f(x + delta x). They also mention the difficulty of doing calculus without understanding the notation.
  • #1
__redzone
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I'm given the limit f(x + [tex]\Delta[/tex]x) / [tex]\Delta[/tex]x
Given f(x) is 2x + 3, do I just plug in 2x +3 into x? Or do I plug it into x and [tex]\Delta[/tex]x, or do I find the limits of f(x + [tex]\Delta[/tex]x) / [tex]\Delta[/tex]x) and -f(x)/[tex]\Delta[/tex]x?, etc..If someone could get me started on this it would be great, Thanks.
 
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  • #2
First of all, write your problem CORRECTLY from your book. That you haven't done.
 
  • #3
This is my first time using latex so I guess I'll just type it out for clarity. Find the limit of the function (f(x + delta x) - f(x)) / delta x as delta x approaches 0 when f(x) = 2x + 3.
 
  • #4
Quite so.
Given that, what is in this case f(x+delta x)?
 
  • #5
You are going to find it very, very difficult to do calculus if you don't understand what "f(x)" and "f(x+ y)" mean!

If f(x)= 2x+ 3, then f(a)= 2a+ 3 (just replace x in the entire formula with whatever is in the parentheses on the left). In particular, f(x+ y)= 2(x+ y)+ 3= 2x+2y+ 3.

(Your latex was fine in your first post. arildno's point was that you didn't specify "as [itex]\Delta[/itex]x goes to 0"!)
 
  • #6
Actually, he did not subtract f(x) in the numerator; that's what I reacted upon.
 

FAQ: Solving Simple Limits with Examples

What is the definition of a limit?

A limit is a mathematical concept that describes the behavior of a function as its input approaches a certain value. It is the value that a function approaches as its input gets closer and closer to a particular value.

Why is it important to solve limits?

Solving limits helps us understand the behavior of a function and its value at a specific point. This is crucial in many areas of science, including physics, engineering, and economics, where we need to know the exact value of a function at a certain point in order to make accurate predictions and decisions.

What are the different types of limits?

The two main types of limits are one-sided limits, where the input approaches the particular value from one side only, and two-sided limits, where the input approaches the particular value from both sides. Other types of limits include infinite limits, where the function approaches positive or negative infinity, and limits at infinity, where the input approaches infinity.

How do I solve simple limits?

To solve simple limits, you can use direct substitution, algebraic manipulation, or graphical methods. Direct substitution involves plugging in the particular value into the function and evaluating the result. Algebraic manipulation involves simplifying the function until you can use direct substitution. Graphical methods involve analyzing the graph of the function to determine its behavior at the particular value.

Can you provide an example of solving a simple limit?

Sure, let's say we have the limit of (x^2-4)/(x-2) as x approaches 2. Using direct substitution, we get (2^2-4)/(2-2) = 0/0. This is an indeterminate form, so we can use algebraic manipulation. Factoring the numerator, we get ((x+2)(x-2))/(x-2). Canceling out the common factor of (x-2), we are left with x+2. Now we can use direct substitution again and plug in x=2 to get the final result of 4.

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