Question

Are limits used to find derivatives/slope?

Answer 1

Lol ok as I said I get what you are trying to say. The really long definition of a derivative uses a limit. Does this look familiar?

\[f'(x) = \lim_{h \rightarrow 0}\frac{ f(x+h) - f(x) }{ h }\]

Answer 2

yeahhhh I think my calc teacher just began teaching us that last week. The slope of a tangent line

Answer 3

Correct this is the limit of the difference quotient. How ever, the two terms are different in meaning. I will use an example to show this.

f(x) = 2

This is nice and simple so.

\[\lim_{x \rightarrow a} f(x) = 2\]

Since as x goes to any point a it is still two since y = 2 is a horizontal line

Now the derivative of f(x) is 0 since the derivative of a constant is 0. As you can see the two results differ meaning they do not mean the same thing

Answer 4

oooh I understand now hehe thanks so much. I've been learning how to find the derivatives, but I wasn't really understanding why or the purpose but now I feel like I am understanding the whole concept ^_^

Answer 5

Yea the limit of the difference quotient is just used to get the function only in terms of x and not x and h or in some classes x and delta x

Answer 6

I have another question lol, in Calculus, you have to find the slope of a curve, that's the goal or purpose right. Does it mean that you can only find the slope between two points? or only as it is approaching a certain value? Is that why we use limits?

Answer 7

Eventually you will learn how to take a derivative without using limits. You learn a few rules known as the Power Rule, Sum and Difference Rule (Which ties into Power Rule easily), Product Rule, Quotient Rule, and The Chain Rule (aka Extended Power Rule)

Answer 8

oh ok :) thanks so much

Answer 9

And the goal of calculus depends on what side of calculus you are learning. Calculus has two groupings. Differentiation and Integration. Right now you are learning the first half

Answer 10

oooh cool :D

Answer 11

Ya Integration is just Anti-Derivatives