Finding Limits with a Constant: Tips for Calculus Students

In summary, the conversation is about finding the limit of the expression (8(a+h)^2 - 8a^2)/h as h approaches 0 in terms of the constant a. The person asking for help is unsure how to approach the problem and mentions some topics they have covered in calculus. The person providing help suggests substituting h=0 and expanding the numerator to eventually cancel out the h in the denominator. The final answer is 16a, but the person asking for help does not fully understand it at first.
  • #1
EvilBunny
39
0

Homework Statement



Find in terms of the constant a

Lim h --- > 0

8 (a+h)² - 8a²
-----------------
h


The Attempt at a Solution



I have no idea how to even approach it so some pointers would be nice.
It hasn't been long since I started calculus. I am not sure weather we covered this
or not , classes are so heavy with content and passes quickly :s .

anyways what I am sure we have seen until now is

-IVT
- squeeze
- Limit laws

we have seen some things concerning continuity theorems altho am currently lost in them.
 
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  • #2
Well,if you substitute in the value of h=0 directly, then you will get 0/h = 0.
So, why don't you try to expand the numerator? Then, proceed to the operations and eventually, the h at the denominator will be canceled out.
 
  • #3
well I end up with 16a = something . am giong to look at it more
 
Last edited:
  • #4
huh.. well the answer Is 16a altho I don't really understand it.
 
  • #5
Ooo I get it now well thanks for your time.
 

FAQ: Finding Limits with a Constant: Tips for Calculus Students

What is a limit with a constant?

A limit with a constant is a mathematical concept that describes the behavior of a function as the input values approach a specific number, known as the constant. It is used to determine the value of the function at that particular number.

How is a limit with a constant calculated?

A limit with a constant is calculated by evaluating the function at values approaching the constant from both sides. The limit is then the value that the function approaches as the input values get closer and closer to the constant.

Why is a limit with a constant important?

A limit with a constant is important because it helps us understand the behavior of a function at a particular point. It allows us to predict the value of the function at that point and also helps in solving more complex mathematical problems.

What are the common notations used for a limit with a constant?

The common notations used for a limit with a constant are lim (an abbreviation for limit), an arrow notation (→), and infinity notation (∞).

Can a limit with a constant have multiple solutions?

No, a limit with a constant can only have one solution. This is because the limit represents the value that the function approaches as the input values get closer and closer to the constant, and there can only be one value that the function approaches at a specific point.

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