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znimon
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A function is given below. Determine the average rate of change of the function between x = 3 and x = 3 + h. f(t) = √7t
 2 years ago
 2 years ago
znimon Group Title
A function is given below. Determine the average rate of change of the function between x = 3 and x = 3 + h. f(t) = √7t
 2 years ago
 2 years ago

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znimon Group TitleBest ResponseYou've already chosen the best response.0
I have \[\sqrt{7h}/h\] but it says that is wrong and I can't figure out why
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
Well, the 'average' rate of change for some interval \([a,b]\) (noncalculus, please tell me if you need otherwise) would be: \[ \Delta f_{avg}=\frac{f(b)f(a)}{ba} \]Try using that.
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
This is precalc
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
All right, then that should be the case.
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
so you are telling me my answer is right?
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
Nope, sorry. Using the above, we find, for \(f(t)=\sqrt{7t}\) \[ \frac{f(3+h)f(3)}{3+h+3}=\frac{\sqrt{217h}\sqrt{21}}{h} \]If you need further simplification of the above, please tell me.
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
how did you get 7h out from under the root?
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
How does one? You can't, you'd have to multiply both the numerator and denominator by \(\sqrt{217h}+\sqrt{21}\), but then it would end up on the denominator.
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
This is only useful for evaluating the limit.
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
I have no idea what you mean by that
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
why would I multiply the numerator and denominator by that?
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
My 7 sub 2 is \[\sqrt{217h}\]
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
If you wish to remove the \(h\) from the radical, you'd have to do that, but, of course, then the top expression ends up in the denominator. So, the point is that one cannot remove the \(h\) from such.
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
yours simplifies to 7
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
f(3+h) = \[\sqrt{7(3+h)}\]
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
My equation does not simplify. And, yes, that last statement is correct. Keep in mind: \[ \sqrt{a+b}\sqrt{a}=\sqrt{b}\\ \]Is *not* necessarily true (In fact, it is mainly true if b=0 or a=0).
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
The original problem looks like the square root goes over the "t"
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
Yes, and that's how I computed it. What do you feel is wrong with my expression?
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
I don't understand how there is no square root sign over the 7h in your third comment
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
Where is there not a square root sign?
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
Over the "7h"
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
the 7h that is in the numerator of your third comment
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
http://imgur.com/1fwvB This is what I have in my browser and what has been typed.
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
oh that is weird it doesn't look like that in my browser
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
so my first comment is correct then
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
Square root of (7h) divided by h
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
No, it is not, as they are not equivalent statements.
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
yeah it is because square root of (x+y) is equal to square root of x plus square root of y right?
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
No, it does not. \[ \sqrt{a+b}\ne\sqrt{a}+\sqrt{b} \]Unless a or b is zero.
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
oh jesus I feel like an idiot. So then your third comment does not simplify any further in pre calc?
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
Nope. I don't think there is any need to, unless you're taking limits.
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
so last thing square root of x*y is equal to square root of x times the square root of y?
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
Never mind I just proved it.
 2 years ago

znimon Group TitleBest ResponseYou've already chosen the best response.0
Thanks again I'll have to look up a khan academy video on that
 2 years ago

LolWolf Group TitleBest ResponseYou've already chosen the best response.1
Yes, that statement is true. Since: \[ a^2=n\\ b^2=m \]So we say: \[ nm=a^2b^2=(ab)^2 \]And all right, sure thing.
 2 years ago
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