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needhelp07
Group Title
Problem :
Find the derivatives of the function using the limit of definition
y=x^4
 one year ago
 one year ago
needhelp07 Group Title
Problem : Find the derivatives of the function using the limit of definition y=x^4
 one year ago
 one year ago

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irkiz Group TitleBest ResponseYou've already chosen the best response.0
still the same type of question? try going http://www.math.hmc.edu/calculus/tutorials/limit_definition/ they show you examples. just apply your question to how they solve it.
 one year ago

irkiz Group TitleBest ResponseYou've already chosen the best response.0
It cant be that you were taught 2 other similar questions but still cant solve it.
 one year ago

needhelp07 Group TitleBest ResponseYou've already chosen the best response.0
im confused about the exponent 4
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
do you know how to do (a+b)^4?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
its the binomial theorem or pascal triangle
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 etc....
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
for example just look at the pascal triangle for the coefficients (a+b)^2= 1a^2 + 2ab +1b^2= a^2 +2ab+b^2 can you guess whats (a+b)^3? and for (a+b)^4?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
note it can be like (x+y)^3 ? or (x+y)^4 ?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
so power of 3 we get the coefficients of 1 3 3 1 therefore the answer for (x+y)^3= x^3 +3x^2y +3 xy^2 + y^3 can you guess for (x+y)^4 ?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
the reason i want you to learn this is when you go solved for the derivative of y=x^4 you will get to find (x+y)^4
 one year ago

needhelp07 Group TitleBest ResponseYou've already chosen the best response.0
tnx a lot . i need to study more about this
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
im here now to teach you the easier way of doing it
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
ok for the power of 4 the coefficents inthe pascal triangle are 1 4 6 4 1 therefore (a+b)^4 = a^4 + 4a^3 b +6 a^2 b^2 +4 a b^3 + b^4 or (x+y)^4= x^4 +4x^3 y + 6 x^2 y^2 + 4x y^3 + y^4 did you see it ?
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
now for practice y=x^2 \[y+\Delta y=x +\Delta x\] \[\Delta y=x+\Delta x  y\] \[\Delta y= (x+\Delta x)^{2}x ^{2}\]
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
can you try solving that first ?
 one year ago

needhelp07 Group TitleBest ResponseYou've already chosen the best response.0
i try solving it
 one year ago

needhelp07 Group TitleBest ResponseYou've already chosen the best response.0
the answer is 2x
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
\[\Delta y=f(x+\Delta x)  y\] \[\Delta y=(x+\Delta x)^{2} x ^{2}\] \[\Delta y= x ^{2 }+ 2x \Delta x +\Delta x ^{2} x ^{2}\] add or subtract we get \[\Delta y= 2x \Delta x+\Delta x ^{2}\] now the derivative is \[y'=f'(x)= \lim _{\Delta x >0}\frac{ \Delta y }{ \Delta x }=\] \[= \lim _{\Delta x>0}(\frac{ 2x \Delta x+\Delta x ^{2} }{ \Delta x })\] try to cancell something in there
 one year ago

needhelp07 Group TitleBest ResponseYou've already chosen the best response.0
i know it already the answer is 2x
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
ok good can you try it if its y=x^4 ? do the same process
 one year ago

needhelp07 Group TitleBest ResponseYou've already chosen the best response.0
the answer is 4x^3+6x^2+4x
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
hmm to make it easier lets make delta x=h so that delta y=(x+h)^4  x^4 try solving that first
 one year ago

needhelp07 Group TitleBest ResponseYou've already chosen the best response.0
I cant follow my professor's teaching. Good to know that u are here to help me .thank you so much. you are a great help! i need to do more assignments about this so i will go out now .
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
the answer should be f'(x)=4x^3
 one year ago

needhelp07 Group TitleBest ResponseYou've already chosen the best response.0
haha im wrong
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
do the process i gave you there, and you will arrive at the correct answer ... :D
 one year ago

needhelp07 Group TitleBest ResponseYou've already chosen the best response.0
i wish i have a tutor like u hahaha .
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
remember this ?. (x+y)^4= x^4 +4x^3 y + 6 x^2 y^2 + 4x y^3 + y^4 make y an h here so that (x+h)^4= x^4 +4x^3 h + 6 x^2 h^2 + 4x h^3 + h^4
 one year ago

needhelp07 Group TitleBest ResponseYou've already chosen the best response.0
anyway thx a lot
 one year ago

needhelp07 Group TitleBest ResponseYou've already chosen the best response.0
goodbye!
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
ok just read it through here again and learn from it good luck and have fun now :D
 one year ago

mark_o. Group TitleBest ResponseYou've already chosen the best response.1
ok just messege me here and if you have prob i will go and give you an advise or correct if you have something done incorrectly ... :D
 one year ago
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