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IsTim
 3 years ago
Find the equation of the tangent to the curve at the given x value.
IsTim
 3 years ago
Find the equation of the tangent to the curve at the given x value.

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IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0I got up to this:dw:1335261401688:dw

chaise
 3 years ago
Best ResponseYou've already chosen the best response.2Calculate the derivative of the equation, make the equation to equal, solve it and plug in your x value. Are you familiar with the quotient rule in derivatives?

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Deriatives is f'(x) right? we're not doing that yet.

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Methods we're using is substitution, factoring and the conjugate method.

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0I'm using the Calculus Phobe videos from Calculus Help (my teacher showed me the website and told me to use that).

chaise
 3 years ago
Best ResponseYou've already chosen the best response.2Yes, that's correct. So you're differentiating using the definition? If you take the derivative of the equation y=3/(x^21) you can find the slope. if: f(x)=3/(x^21) then f(x+h)=3/((x+h)^21) dy/dx = (f(x+h)f(x))/h Can you do the rest?

chaise
 3 years ago
Best ResponseYou've already chosen the best response.2dy/dx =lim (h>0) (f(x+h)f(x))/h rather.

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0But I can't go any further. dw:1335262087563:dw That's the furthest I got up to.

chaise
 3 years ago
Best ResponseYou've already chosen the best response.2Expand your brackets and factor out a h.

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0The bottom one to? I was told not too.

chaise
 3 years ago
Best ResponseYou've already chosen the best response.2Not sure  I'm not familiar with the long method, I just use the shortcut :)

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1Can you take derivatives? Must you use first principle to find it?

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Derivatives is our next unit.

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0I can't isolate or factor out anything. I must had made a mistake beforehand I guess.

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1I hope you don't mind me posting my solution here

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0I guess not, but it's notm much like my work.

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1Oh shoot... I got some mistakes there! Wait

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1Oh my dear!!! The final answer should be 4/3 ... not 2 as I've written :S

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1Is your question \[\frac{3}{x^21}\] or \[\frac{3}{x^2+1}\]?

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Maybe I should upload my work, and maybe you check for problems?

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Starting from c) at Scan001.

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0but since x=2, I subbed in a=2 into that equation...

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1for the denominator, (a+h)a =h , not a+h 2 You need to find the limit before substituting the numbers.

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1After you've found the limit, you'll see the unknown x. By then, sub x=2 and you'll get the slope. But NOT when you're taking the limit

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0I thought the unknown to be m, and that h was still the variable withint the equation?

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1h is something you need to deal with. Should I upload an example to should how you do first principle for you ?

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0I've got an example here with me from my teacher.

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1If you don't need it, it's okay :) Should I keep checking for you or you want to do corrections first?

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1Correct starting from the third line For numerator: a > 3/ (a^2 1) For denominator: a+h2 > h (in your previous step, a+h a, simplify it , you'll get h)

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Sorry if I sound ignorant, but that's how I saw it in the example...the h is alone.

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1Do you mind uploading your example also?

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1First, the situation is different . You're given 2 values there, but only 1 here. Second, to be frank, I don't understand what you (or your teacher) is doing. It's not the normal way as I've learnt.. Third, I still insist that you shouldn't sub the value immediately...

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Ok. I think I know what you are doing, and what my teacher is doing. You're going from a general formula, while my teacher is using the specific formula. The general formula doesn't sub in the x or a value until the end.

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1It's good that you notice the difference :)

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Just looking through my notes I guess. I've got a test coming up, so I thought reviewing would be best.

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2well, where do you need help with? This is pretty long..

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Maybe I should just leave this question. I tried this for over 2 hours by now.

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2First, what is the question? \[\frac{1}{x2} \]?? or \[\frac{3}{x^{2}1} \]??

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Ok. Thanks for the attempt guys. I'll try other problems, and maybe this might make more sense.

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2wait..i will try and do it first.. can't you take the derivative which is easier?

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Others suggested that, but that's for the next unit. I understand a bit on how that works, but I'm not allowed using it here.

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2Hmm..I might try it but it might take a while since i havent done these in a while...

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Ok. Well, I guess you can do so, if yo uhave free time. But most likely you too have something important coming up (immediately).

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2No, I don't have anything important..i might be able to do it but not sure..lol

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2I have to review these anyway

apoorvk
 3 years ago
Best ResponseYou've already chosen the best response.0^^That was mammoth. phew. Istim do you know how to differentiate using chain rule?

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2lol, i failed...do you remember how to do these apoor? my brain is failling me :(

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0No, I don't (Sorry, cleaning up house).

apoorvk
 3 years ago
Best ResponseYou've already chosen the best response.0Hmm. so you want to do this by the first principle of finding derivatives okay.

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0I am just oh so selective in the method used. That be the end of me.

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2\[\large\frac{f(x+h)f(x)}{h} =>\frac{\frac{3}{(x+h)^{2}1}\frac{3}{x^{2}1}}{h} \]

chaise
 3 years ago
Best ResponseYou've already chosen the best response.2should be the limit as h approaches zero, but, apart from that, correct. ^_^

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2\[\large =>\frac{\frac{3}{h^{2}+2hx+x^{2}1}\frac{3}{x^{2}1}}{h} \] \[\large >\frac{\frac{3(x^{2}1)3(h^{2}+2hx+x^{2}1)}{(h^{2}+2hx+x^{2}1)(x^{2}1)}}{h} \]

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2I think that im doing it wrong..i dont think that its this complicated..

chaise
 3 years ago
Best ResponseYou've already chosen the best response.2Perhaps you should just use quotient rule.

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2but it says derivatiive thing is not allowed..

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Before using deratives. Referencing Calculus Phobe from Calculus Help. I think I used Conjugate Method.

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2whaat..im lost..i looked at your example but it got confusing..then i looked at my book its more confusing..using the chain rule is easier.

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.2\[\frac{3}{x^{2}1} => 3(x^21)^{1}\] \[3(x^21)^{1}*2x \] \[6x(x^21)^{1}\] easier i suppose..
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