How solve the instantaneous rate

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In summary, the conversation is about solving a limit and finding the instantaneous rate of change using calculus. The participants discuss different methods, such as the quotient rule and the power rule, and give advice on learning calculus. They also recommend finding a book that explains the concepts clearly.
  • #1
janemba
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how solve a limit

do anyone how do you solve a limit how work because I am beginning this here's one problom

y= [tex]\overline{}2x[/tex]
x+1
 
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  • #2
[tex]y=\frac{2x}{x+1}[/tex] is this what u wrote?

And you want to find the instantaneous rate of change, right?

Any thoughts from your side on how to do it?
We are not supposed to do your homework!

EDIT: to find the instantaneous rate of change you need to evaluate the limit
[tex]lim_{h\rightarrow\ 0}\frac{f(x+h)-f(x)}{h}[/tex] which actually is the derivative of that function! Assuming that this function represents the velocity!
 
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  • #3
yes

yes it is and yes I am trying to find the instantaneous and it is not homework i want to learn how you solve it step by step
 
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  • #4
janemba said:
yes it is

Have you given any thoughts so far on how to do it? SHow us what have u done so far, so someone here might point u on the right direction. People here won't just give you the answer, especially here at the Homework Forum!
 
  • #5
Um

the truth is I am 14 and i want to be the smartest person on Earth and want to be physics professor so i figure you have to learn calculus before going into QUANTUM PHYSICS
 
  • #6
janemba said:
do anyone how do you solve a limit how work because I am beginning this here's one problom

y= [tex]\overline{}2x[/tex]
x+1

Well, are u trying to find the limit or the instantenaous rate of change? Because i do not see any limits here?? Can you post the whole question first?
 
  • #7
janemba said:
the truth is I am 14 and i want to be the smartest person on Earth and want to be physics professor so i figure you have to learn calculus before going into QUANTUM PHYSICS

I do not think quantum physics is taught at high school is it?
I envy you for trying to deal with these things at this age! well, i must ask you again, are you trying to find some kind of limits, or what? Because you edited your original post, so i do not know what exactly are you looking for! then i might try to point you on the right direction!
 
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  • #8
in college

no way its taught in college but you start learning about physics
 
  • #9
how

how do you evaluate instantaneous rate of change and where is the derivative
 
  • #10
janemba said:
how do you evaluate instantaneous rate of change and where is the derivative

Hi there! Welcome aboard! I too admire your enthusiasm. It is hard, though, to tell where to start, especially without knowing your background in mathematics. If you have a strong background in algebra and geometry, that will definitely help.

I would suggest searching around online first like http://en.wikipedia.org/wiki/Derivative" and seeing what you can extrapolate for yourself. Then come on back here to PF and show us exactly where you are having trouble.

Do you understand what the derivative means? If not, do a little reading in Wiki or elsewhere and come back with questions.

Hope to hear from you soon!
 
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  • #11
I

I Only Know The Power Rule To Find Dervitives But Geometry I Get
 
  • #12
Google "the quotient rule" and see what you get. Come back with questions.
 
  • #13
is that how you do it because i Google the quiotent rule but just didn't know what it meant

\frac{d}{dx}f(x) = f'(x) = \frac{h(x)g'(x) - g(x)h'(x)}{[h(x)]^2}.
 
  • #14
janemba said:
is that how you do it because i Google the quiotent rule but just didn't know what it meant

\frac{d}{dx}f(x) = f'(x) = \frac{h(x)g'(x) - g(x)h'(x)}{[h(x)]^2}.

The deal is that if you really want to learn this material, then you have to start from something that is really elementary, and do things one step at a time! so if you have no idea what a limit is, and what a derivative is, then my advice is buy a book that is really elementary but that will introduce you to some quite important concepts!
 
  • #15
I'd recommend reading the theory behind derivatives as rate of change, and it's geometric significance. And one more thing, be thorough with the concept of limits (not just some list of formulas), so that you can understand the "first principle" of derivatives and other elementary concepts.

Here is a link to a complete video series on Calculus by Houston University,

http://online.math.uh.edu/HoustonACT/videocalculus/

Regards,
Sleek.
 
  • #16
yea

i have a book about calculus its called super review calculus all you need to know but its just confusing
 
  • #17
Unfortunately, we cannot just teach you calculus. We can help you along, but you need to work through a lot of it on your own. You should find a different book to learn from. Like one of the demystified books. Something that explains the concepts. Then you can try to apply them to the specific problems.
 
  • #18
ok i have on the link on 1 page
 

What is the instantaneous rate?

The instantaneous rate refers to the rate at which a quantity is changing at a specific moment in time. It is also known as the derivative or slope of a curve at a particular point.

Why is it important to solve for the instantaneous rate?

Solving for the instantaneous rate allows us to understand the behavior of a quantity at a specific point in time. It is useful in many scientific and mathematical applications, such as predicting the speed of an object at a given moment or determining the growth rate of a population.

How do you solve for the instantaneous rate?

To solve for the instantaneous rate, you need to find the derivative of the function representing the quantity. This can be done using various mathematical techniques, such as the limit definition or the power rule.

What are some real-life examples of using the instantaneous rate?

The instantaneous rate is used in many fields, such as physics, biology, and economics. For example, in physics, it can be used to calculate the acceleration of an object at a particular time. In biology, it can be used to analyze the growth rate of a population. In economics, it can be used to determine the rate of change of a stock's value.

What is the difference between average rate and instantaneous rate?

The average rate is the average change of a quantity over a given period of time, while the instantaneous rate is the rate of change at a specific moment in time. The average rate gives an overall picture of the change, while the instantaneous rate gives a more detailed understanding of the change at a particular point.

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