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 one year ago
Dear, Mathtalent!
The slope of the tangent line to the graph of the function y=3x^3 at the point (381) is limx=>3 (3x^3−81)/(x3.) By trying values of x near 3, find the slope of the tangent line
 one year ago
Dear, Mathtalent! The slope of the tangent line to the graph of the function y=3x^3 at the point (381) is limx=>3 (3x^3−81)/(x3.) By trying values of x near 3, find the slope of the tangent line

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ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Take you calculator and try x=2.9, 2.99, 2.999, to get a good idea where this is going to...

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0ok,Thank you. I have a calculator with me.. but why x=2.9??

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0oh i get it beacuse its near 3....

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Well, you want to know the limit for x > 3. You are not supposed to do all kinds of math trickery to do this, but just try a few values near 3. So 2.9, or 3.1 and then even closer: 2.99 or 3.01, or any other value, as long as it is "near" 3...

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0Once I gt all answers from equation. what shall I do?

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Can you guess what the number is that you are getting closer and closer to?

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0hmmmm I will try put 2.9 , 2.999 in the equation first Please hold!

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0Ok, So I got 78.33 for x=2.9 and 80.7303 for x=2.99... I guess it gets closer to 81?

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0cuze at the point (3, 81)

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1It does, so it's a safe bet 81 is the slope of the tangent line!

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1(3,81) begin the point on the graph is in itself not of importance. By coincidence, the ycoordinate is also 81.

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0Omg, thats prety cool! thank you very much :) are you faimilar with Tagent Velocity:

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1You mean the velocity of a moving point along a curve is the tangent vector? Or is it a book? (havent't got a clue here..)

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1I could be familiar with the stuff in the book ;)

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0cool. The displacement (in meters) of a particle moving in a straight line is given by s=3t^3 where t is measured in seconds. 1)Find the average velocity of the particle over the time interval [7,10]. 2)Find the (instantaneous) velocity of the particle when t=7

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Do you know the difference between average velocity and instantaneous velocity?

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0mmm No. I have no idea. av velo =displacement/ time elapsed?

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1It is, so that one is easy. Just calculate (s(10s(7))/(107).

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1For instanteneous velocity, you'll have to do the limitstuff as in the first problem. Can you write down the limit?

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0so s(10)s(7)/3? for the fist one?

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Yes, because s(10s(7) is the distance you've travelled.

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0and jusy plug s=3t^3 in s?

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Don't get what you're saying there...

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1s(10)=3*10³=3000, s(7)=3*7³=1029 (30001029)/3=657 m/s (you may not be using meters, but feet...)

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0For instanteneous velocity, I have to do limit thing? x=>7?

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Write down the limit:\[v(7)=\lim_{t \rightarrow 7}\frac{ s(t)s(7) }{ t7 }\] and try numbers near 7.

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0OK, I tired to 6.99. s(6,99)=(6.99)^3*3=1024.59 S(7)= 1029 1024.591029/10297?

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1You have to divide by t7, which is 6.997=0.01

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1441 is good. Just use brackets...

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Oh, now I get it ;) If you set t=6.999 you'll be even closer to 441, so that will be the answer

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0Oh! So limit is how you get closer to x or function?

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Yes, it is the value of a formula as you get closer and closer to a certain number. Only, because of the special kind of formula, it is not possible to try that number directly. As in the formula above: if you want the speed at t=7, you can't just put t=7 and get the right answer. If you try it, you'll get 0/0, which is undefined.

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1It is possible however, to do more advanced calculations with the formula to get the limit. It is called differentiation... Once you know how to do that, you don't need to try all these cumbersome numbers "near" to a certain value!

Dodo1
 one year ago
Best ResponseYou've already chosen the best response.0Wow, thank you so much for your detailed explaination. It is really fun doing math with you!

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Thanks for the compliment! I really appreciate it.
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