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anonymous
 4 years ago
limit
anonymous
 4 years ago
limit

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1350454227197:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1350454341729:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes i think so that doesnt cancel out tho . im making a mistake

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1\[\huge \lim_{h \rightarrow 0}\frac{[(x+h)^{3}3](x^{3}3)}{h}\] is this it?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yupp ! how do you make it big like that btw ?

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1uhh, before typing in your equations and stuff, put in \huge

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1This looks like you're taking the derivative of \[\huge x^{3}  3\]

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1And you're to get the derivative using limits? lol, that's harsh... :D

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1You'll realise soon that there are faster ways of getting the derivative... anyway, just evaluate the numerator and show me what you get...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0x^3 's cancel 3's cancel... what's left?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.03x^2h + 3xh^2 +h^3 all divided by h factor out an 'h' in the numerator cancel with the 'h' in the denom. now you can take the limit without issues.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\huge \ \frac{ x^3+3x^2h+3xh^23x^2+3 }{h }\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i have an x^3 and x^2 ? :S

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1Well that changes everything...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ f(x+h)  f(x) }{h }\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{(x+h)^3 3  ( x^3 3) }{h }\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thats why it doesnt cancel out

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you expanded correctly: \[\frac{ x^3 +3x^2h +3xh^2 +h^3 3  (x^3 3) }{h }\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0then why are you cubing (x+h) ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ohhh i should square it *facepalm*

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ (x+h)^2 3 (x^23) }{h }\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0can you help me with this one: find the equation of the tangent \[y=\frac{ x2 }{ x+2 }\] when x=0

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\huge \lim_{h \rightarrow 0} \frac{ (x+h)2 }{ (x+h)+2 } \frac{ x2 }{ x+2 }\]

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1Equation of the tangent involves derivatives, right?

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1Quotient rule? Ever dabbled with it?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0no we're not allowed to use that yet .

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1Here, I don't think I have the attention span to type this out o.O http://www.math.hmc.edu/calculus/tutorials/quotient_rule/proof.pdf

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1You're allowed to use anything as long as you can prove it ;)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0my tests always state "Only using method thought in class" i know that quotient rule is so much faster

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0and we we're never thought that in class yet

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1Well, don't despair :D I'll see what I can do... To get the equation of the tangent line, first we need a slope. to get that slope, we need the derivative. So what's the derivative (go ahead and express it first in limitform)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\huge \lim_{h \rightarrow o}\frac{ (x+h)2 }{ (x+h)+2 }  \frac{ x2 }{ x+2 }\]

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1nope... you forgot that all that must also be divided by h... small details, but no less important...

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1tsk \[\huge \lim_{h \rightarrow 0}\frac{\frac{ (x+h)2 }{ (x+h)+2 }  \frac{ x2 }{ x+2 }}{h}\]

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1Right, well this can also be written as \[\lim_{h \rightarrow 0}\frac{1}{h}\left( \frac{ (x+h)2 }{ (x+h)+2 }  \frac{ x2 }{ x+2 } \right)\]

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1now \[\lim_{h \rightarrow 0}\frac{1}{h}\frac{\left[ \left( x+h \right)2 \right]\left( x+2 \right)\left[ \left( x+h \right)+2 \right]\left( x2 \right)}{\left[ \left( x+h \right)+2 \right]\left( x+2 \right)}\] o.O

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0wait, how did you get rid of those fractions ?

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1Like magic :P \[\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}\]

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1Hey, there's nothing you can cancel...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0then expansion and cancelling out the like terms

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1Nothing that would you do you much good, anyway... Here's a tricky bit of manipulation \[\lim_{h \rightarrow 0}\frac{1}{h}\frac{\left[ \left( x+h \right)2 \right]\left( x+2 \right)(x2)(x+2)+(x2)(x+2)\left[ \left( x+h \right)+2 \right]\left( x2 \right)}{\left[ \left( x+h \right)+2 \right]\left( x+2 \right)}\]

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1All right, scratch everything, I overlooked one important detail...

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1You only need to get its slope on the specific case where x = 0 right?

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1Use this definition of derivative instead: \[f'(c)=\lim_{x \rightarrow c}\frac{f(x)f(c)}{xc}\]

terenzreignz
 4 years ago
Best ResponseYou've already chosen the best response.1Sorry for this extremely late reply, I was busy with something :( c is 0.
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