Delete
Share
This Question is Closed
burhan101
Best Response
You've already chosen the best response.
0
|dw:1350454227197:dw|
burhan101
Best Response
You've already chosen the best response.
0
|dw:1350454341729:dw|
terenzreignz
Best Response
You've already chosen the best response.
1
Lol, derivative?
burhan101
Best Response
You've already chosen the best response.
0
yes i think so
that doesnt cancel out tho -.- im making a mistake
terenzreignz
Best Response
You've already chosen the best response.
1
\[\huge \lim_{h \rightarrow 0}\frac{[(x+h)^{3}-3]-(x^{3}-3)}{h}\]
is this it?
burhan101
Best Response
You've already chosen the best response.
0
yupp ! how do you make it big like that btw ?
terenzreignz
Best Response
You've already chosen the best response.
1
uhh, before typing in your equations and stuff, put in \huge
burhan101
Best Response
You've already chosen the best response.
0
thanks:D
terenzreignz
Best Response
You've already chosen the best response.
1
This looks like you're taking the derivative of
\[\huge x^{3} - 3\]
burhan101
Best Response
You've already chosen the best response.
0
yup that's right !
terenzreignz
Best Response
You've already chosen the best response.
1
And you're to get the derivative using limits? lol, that's harsh... :D
burhan101
Best Response
You've already chosen the best response.
0
yess i have to
terenzreignz
Best Response
You've already chosen the best response.
1
You'll realise soon that there are faster ways of getting the derivative... anyway, just evaluate the numerator and show me what you get...
Algebraic!
Best Response
You've already chosen the best response.
0
x^3 's cancel
3's cancel...
what's left?
Algebraic!
Best Response
You've already chosen the best response.
0
3x^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.
burhan101
Best Response
You've already chosen the best response.
0
\[\huge \ \frac{ x^3+3x^2h+3xh^2-3-x^2+3 }{h }\]
Algebraic!
Best Response
You've already chosen the best response.
0
no.
burhan101
Best Response
You've already chosen the best response.
0
i have an x^3 and x^2 ? :S
Algebraic!
Best Response
You've already chosen the best response.
0
no.
terenzreignz
Best Response
You've already chosen the best response.
1
Well that changes everything...
Algebraic!
Best Response
You've already chosen the best response.
0
\[\frac{ f(x+h) - f(x) }{h }\]
Algebraic!
Best Response
You've already chosen the best response.
0
what's f(x)?
Algebraic!
Best Response
You've already chosen the best response.
0
x^3 -3
Algebraic!
Best Response
You've already chosen the best response.
0
\[\frac{(x+h)^3 -3 - ( x^3 -3) }{h }\]
burhan101
Best Response
You've already chosen the best response.
0
no f(x)=x^2-3
burhan101
Best Response
You've already chosen the best response.
0
thats why it doesnt cancel out
Algebraic!
Best Response
You've already chosen the best response.
0
you expanded correctly:
\[\frac{ x^3 +3x^2h +3xh^2 +h^3 -3 - (x^3 -3) }{h }\]
Algebraic!
Best Response
You've already chosen the best response.
0
ok
Algebraic!
Best Response
You've already chosen the best response.
0
then why are you cubing (x+h) ?
burhan101
Best Response
You've already chosen the best response.
0
ohhh i should square it *facepalm*
Algebraic!
Best Response
You've already chosen the best response.
0
\[\frac{ (x+h)^2 -3 -(x^2-3) }{h }\]
burhan101
Best Response
You've already chosen the best response.
0
can you help me with this one: find the equation of the tangent \[y=\frac{ x-2 }{ x+2 }\]
when x=0
burhan101
Best Response
You've already chosen the best response.
0
\[\huge \lim_{h \rightarrow 0} \frac{ (x+h)-2 }{ (x+h)+2 } -\frac{ x-2 }{ x+2 }\]
burhan101
Best Response
You've already chosen the best response.
0
@terenzreignz
terenzreignz
Best Response
You've already chosen the best response.
1
Equation of the tangent involves derivatives, right?
burhan101
Best Response
You've already chosen the best response.
0
yes
terenzreignz
Best Response
You've already chosen the best response.
1
Quotient rule? Ever dabbled with it?
burhan101
Best Response
You've already chosen the best response.
0
no we're not allowed to use that yet -.-
terenzreignz
Best Response
You've already chosen the best response.
1
You're allowed to use anything as long as you can prove it ;)
burhan101
Best Response
You've already chosen the best response.
0
my tests always state "Only using method thought in class"
i know that quotient rule is so much faster
burhan101
Best Response
You've already chosen the best response.
0
and we we're never thought that in class yet
terenzreignz
Best Response
You've already chosen the best response.
1
Well, 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 limit-form)
burhan101
Best Response
You've already chosen the best response.
0
\[\huge \lim_{h \rightarrow o}\frac{ (x+h)-2 }{ (x+h)+2 } - \frac{ x-2 }{ x+2 }\]
terenzreignz
Best Response
You've already chosen the best response.
1
nope... you forgot that all that must also be divided by h... small details, but no less important...
burhan101
Best Response
You've already chosen the best response.
0
ohh i did :$
terenzreignz
Best Response
You've already chosen the best response.
1
tsk
\[\huge \lim_{h \rightarrow 0}\frac{\frac{ (x+h)-2 }{ (x+h)+2 } - \frac{ x-2 }{ x+2 }}{h}\]
burhan101
Best Response
You've already chosen the best response.
0
ok yupp
terenzreignz
Best Response
You've already chosen the best response.
1
Right, well this can also be written as
\[\lim_{h \rightarrow 0}\frac{1}{h}\left( \frac{ (x+h)-2 }{ (x+h)+2 } - \frac{ x-2 }{ x+2 } \right)\]
burhan101
Best Response
You've already chosen the best response.
0
oh okayy
terenzreignz
Best Response
You've already chosen the best response.
1
now
\[\lim_{h \rightarrow 0}\frac{1}{h}\frac{\left[ \left( x+h \right)-2 \right]\left( x+2 \right)-\left[ \left( x+h \right)+2 \right]\left( x-2 \right)}{\left[ \left( x+h \right)+2 \right]\left( x+2 \right)}\]
o.O
burhan101
Best Response
You've already chosen the best response.
0
wait, how did you get rid of those fractions ?
terenzreignz
Best Response
You've already chosen the best response.
1
Like magic :P
\[\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}\]
terenzreignz
Best Response
You've already chosen the best response.
1
Get it now?
burhan101
Best Response
You've already chosen the best response.
0
yeaaah ! i do
burhan101
Best Response
You've already chosen the best response.
0
and then cancelling
terenzreignz
Best Response
You've already chosen the best response.
1
Hey, there's nothing you can cancel...
burhan101
Best Response
You've already chosen the best response.
0
then expansion and cancelling out the like terms
terenzreignz
Best Response
You've already chosen the best response.
1
Nothing that would you do you much good, anyway...
Here's a tricky bit of manipulation
\[\lim_{h \rightarrow 0}\frac{1}{h}\frac{\left[ \left( x+h \right)-2 \right]\left( x+2 \right)-(x-2)(x+2)+(x-2)(x+2)-\left[ \left( x+h \right)+2 \right]\left( x-2 \right)}{\left[ \left( x+h \right)+2 \right]\left( x+2 \right)}\]
burhan101
Best Response
You've already chosen the best response.
0
wow o.O
terenzreignz
Best Response
You've already chosen the best response.
1
All right, scratch everything, I overlooked one important detail...
terenzreignz
Best Response
You've already chosen the best response.
1
You only need to get its slope on the specific case where x = 0 right?
terenzreignz
Best Response
You've already chosen the best response.
1
Use this definition of derivative instead:
\[f'(c)=\lim_{x \rightarrow c}\frac{f(x)-f(c)}{x-c}\]
burhan101
Best Response
You've already chosen the best response.
0
whats c ?
terenzreignz
Best Response
You've already chosen the best response.
1
Sorry for this extremely late reply, I was busy with something :(
c is 0.