A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing

This Question is Closed

Astrobuoy
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow a}\frac{ x^{4}a^{4} }{ xa }\] Wolfram says it = 4a^3 I can't see how. :\

Jonask
 one year ago
Best ResponseYou've already chosen the best response.2this is the derivative of the function\[f(x)=x^4\] at x=a don you see why

Astrobuoy
 one year ago
Best ResponseYou've already chosen the best response.0So just power rule it to be 4a^3, skipping any other steps?

Jonask
 one year ago
Best ResponseYou've already chosen the best response.2using \[\lim_{h \to 0}\frac{f(x+h)f(x)}{h}\]

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1That's assuming you've already taken up derivatives...

linshan789
 one year ago
Best ResponseYou've already chosen the best response.0Treat \[x ^{4}a ^{4}\] as \[(x ^{2})^{2}(a ^{2})^{2}\] then it's algebra.

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1Although, if you wish to be a purist, you can factor out the numerator... \[\huge \frac{x^4a^4}{xa}=\frac{(xa)(x^3+ax^2+a^2x+a^3)}{xa}\]And the rest is dandy :D

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.0No need for a derivative. Factor the numerator.

Jonask
 one year ago
Best ResponseYou've already chosen the best response.2i was just giving for a general \[\frac{x^na^n}{xa}\]

Astrobuoy
 one year ago
Best ResponseYou've already chosen the best response.0I did do 4(xa)/(xa) but then that just leaves 4 if xa and xa cancel one another.

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1Yeah... but \[\large \frac{4(xa)}{xa}\ne\frac{x^4a^4}{xa}\]

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.14 there is an exponent, not a factor ;)

Astrobuoy
 one year ago
Best ResponseYou've already chosen the best response.0Ahh yeah, I don't know why I was thinking that lol.

linshan789
 one year ago
Best ResponseYou've already chosen the best response.0dw:1364049326451:dw From here it's simple algebra...

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.0@Jonask And you should find that that \((xa)\) is a factor of \(x^{n}  a^{n}\) for a wonderfully wide range of values of \(n\).

Jonask
 one year ago
Best ResponseYou've already chosen the best response.2hey that was good y did you delete

terenzreignz
 one year ago
Best ResponseYou've already chosen the best response.1Sorry, made a typo \[\large x^na^n=(xa)(x^{n1}+ax^{n2}+a^2x^{n3}+ \ ... \ +a^{n2}x+a^{n1})\] For as long as \[\huge n\in\mathbb{Z}^+\]

Astrobuoy
 one year ago
Best ResponseYou've already chosen the best response.0I'll remember that @terenzreignz :)

S.RaviTeja
 one year ago
Best ResponseYou've already chosen the best response.0use L'Hospitals rule differentiate nr. and dr. and then apply the limit becoz acc. to the rule if we apply the limit we get 0/0 so after applying the rule we get 4a^3

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0This is a form of the limit definition of the derivative that doesn't come up as often, \[\large \lim_{x \rightarrow a}\frac{f(x)f(a)}{xa} \qquad = \qquad f'(a)\] Just something to keep in mind :) Looks like you have plenty of great assistance already though heh

electrokid
 one year ago
Best ResponseYou've already chosen the best response.0yep and since \[x\to a\implies x\ne a\implies (xa)\ne0\] you can safely cancel off the (xa) term from numerator and denominator
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.