Need a clue on limits, have the answer need explanation

In summary, the speaker has a problem with a limit involving a function and is seeking help to understand the steps to solve it. The limit is found to be 6, but the speaker is struggling to understand the process. They are looking for clarification or guidance on the matter.
  • #1
surferbarney0729
32
0
I have grasped everything in the first 2 segments of my limits chapter, but somehow I am missing out on this problem.

lim (f(x)-4)/(x-2) = 1...find lim
x->4 x->4 f(x)

I am missing something very fundamental and can not find an example explanation in my text. I have the answer which is 6, but have no idea the steps to get there.

Any help?
 
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  • #2
swoodward said:
I have grasped everything in the first 2 segments of my limits chapter, but somehow I am missing out on this problem.

lim (f(x)-4)/(x-2) = 1...find lim
x->4 x->4 f(x)

I am missing something very fundamental and can not find an example explanation in my text. I have the answer which is 6, but have no idea the steps to get there.

Any help?

$$lim_{x\rightarrow 4}\frac{f(x)-4}{x-2} = \frac{\lim_{x\rightarrow 4}(f(x))-4}{4-2}=1$$Does that help?
 

What is a limit?

A limit is a mathematical concept used to describe the behavior of a function as its input approaches a certain value. It is represented by a horizontal asymptote on a graph and can also be thought of as the value that a function approaches but never reaches.

Why are limits important?

Limits are important because they allow us to analyze the behavior of a function without having to actually evaluate it at a specific point. They also help us understand the continuity and differentiability of a function, which are important concepts in calculus and other areas of mathematics.

How do I solve a limit?

To solve a limit, you need to use algebraic manipulation, trigonometric identities, and other mathematical techniques to simplify the expression and determine the limit. You may also need to use theorems and definitions, such as the squeeze theorem or the definition of a limit, to evaluate the limit in certain cases.

What are the types of limits?

The three main types of limits are one-sided limits, two-sided limits, and infinite limits. One-sided limits only consider the behavior of a function as its input approaches a certain value from one direction, while two-sided limits consider the behavior from both directions. Infinite limits occur when a function approaches either positive or negative infinity as its input approaches a certain value.

Can limits be used to evaluate discontinuous functions?

Yes, limits can be used to evaluate discontinuous functions. In fact, this is one of the main applications of limits. By taking the limit of a function at a point where it is discontinuous, we can determine the behavior of the function at that point and whether it is continuous or not.

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