Given the limit, find F and A?

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In summary, the conversation is discussing the limit of a function F at a specific number A. The participants are trying to solve for the values of f and a, and suggest using f(x) = x1/4 and a = 16 as possible solutions. They also discuss using the definition of derivative to solve the limit.
  • #1
xzh
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This limit represents the derivative of some function F at some number A.
lim___________ ([4th root (16+h)] - 2)
_____________________________________
h->0_________________h

f = ?
a = ?

I don't know how to solve this? Teacher said it is going to be on midterms but he never went through it. Thanks.

I think a = 0
 
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  • #2
How about f (x) = x1/4, a = 16?
 
  • #3
hmm, how did you get this? thanks!
losiu99 said:
How about f (x) = x1/4, a = 16?
 
  • #4
You should start by writing down the definition of the derivative and comparing it to the given limit. You can find the f(a+h) term by looking at where (_+h)'s occur in the given limit
 

1. What is a limit in mathematics?

A limit in mathematics represents the value that a function approaches as its input approaches a certain point. It is denoted by the symbol "lim" and is a fundamental concept in calculus.

2. How do you find the limit of a function?

To find the limit of a function, you can either use algebraic manipulation or graphing techniques. Algebraically, you can plug in values closer and closer to the given point and see what value the function approaches. Graphically, you can visualize the behavior of the function near the given point and determine the limit.

3. What does "F" and "A" represent in the phrase "Given the limit, find F and A"?

In this context, "F" typically refers to the function whose limit is being found, and "A" refers to the point at which the limit is being evaluated. However, the specific meaning may vary depending on the context of the problem.

4. Why is it important to find the limit of a function?

Finding the limit of a function is important because it allows us to understand the behavior of the function near a certain point. It is also a crucial concept in calculus and is used to solve various mathematical problems and real-world applications.

5. Can limits be used to prove the existence of a function?

No, limits alone cannot prove the existence of a function. However, they can provide evidence for the existence of a function by showing that the function approaches a certain value as its input approaches a given point.

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