Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
MoonlitFate
Group Title
Find the limit: see the attachment. Please, don't throw around the word derivative, just yet.
 one year ago
 one year ago
MoonlitFate Group Title
Find the limit: see the attachment. Please, don't throw around the word derivative, just yet.
 one year ago
 one year ago

This Question is Closed

MoonlitFate Group TitleBest ResponseYou've already chosen the best response.0
I can do the first step, which I think is to rationalize the numerator, but then I get stuck.
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
rationalize the numerator by multiplying top and bottom by the conjugate of the numerator when you do, the \(\Delta x\) will cancel
 one year ago

MoonlitFate Group TitleBest ResponseYou've already chosen the best response.0
Then I get: \[\frac{ 1 }{ \sqrt{x + \Delta x } + \sqrt{x}} \]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
\[\lim_{h\to 0}\frac{\sqrt{x+h}\sqrt{x}}{h}\times \frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}\] \[=\frac{x+hx}{h(\sqrt{x+h}+\sqrt{x})}\] \[=\frac{h}{\sqrt{x+h}+\sqrt{x}}\] \[=\frac{1}{\sqrt{x+h}+\sqrt{x}}\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
lol i was writing instead of looking at what you wrote
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
now take the limit by replacing \(\Delta x\) by \(0\) and get \[\frac{1}{2\sqrt{x}}\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
which happens to be the "DERIVATIVE" (yeah, i know) of \(\sqrt{x}\) a good one to memorize
 one year ago

MoonlitFate Group TitleBest ResponseYou've already chosen the best response.0
Wow. Funny how the small steps confuse me, yet, I can do most of the "hard" things...
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
true, you did all the hard work replacing \(\Delta x\) by zero is rather simple
 one year ago
See more questions >>>
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.