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

This Question is Closed

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.2What's your plan? \(\int\limits_{0}^{x}f(x)\;dx = F(x)  F(0)\) where \(F(x)\) is an antiderivative of \(f(x)\). \(\dfrac{d}{dx}(F(x)=F(0)) = F'(x) = f(x)\) Isn't that interesting?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.2* "=" in the parentheses should be "". F(x)  F(0)

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.2* Wow! I must be sleeping. I used 'x' two different ways, too! Okay, now that I've confused you. let's just show you. \(\dfrac{d}{dx}\int\limits_{0}^{x}\sin(\sqrt{t^{2}\pi^2})\;dt = \sin(\sqrt{x^{2}\pi^2})\) Ponder on it.

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.2Well, what do you do with a derivative when you want the slope of a tangent line?

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \dfrac{d}{dx}\int\limits\limits_{0}^{x}\sin(\sqrt{t^{2}\pi^2})\;dt = \sin(\sqrt{x^{2}\pi^2})\] You remember how to do that part from earlier, right @onegirl ?

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.1We need a tangent line y = mx+b So to find the tangent line at x=0, we need the slope of the line m... we've already differentiated it above, now we need to find m by plugging in x=0. Then we find b by using the original function in the question.

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.1@tkhunny you put the equation in wrong ( where a + should be), and i copied it wrongly... should be \[\large \dfrac{d}{dx}\int\limits\limits_{0}^{x}\sin(\sqrt{t^{2}+\pi^2})\;dt = \sin(\sqrt{x^{2}+\pi^2})\]

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.2Ah, well that's silly. Why would I do that? Good call!

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.1@onegirl did you get the slope m by putting x= 0 into \[\large m = \sin(\sqrt{x^{2}+\pi^2})\] Then find b by using \[\large \dfrac{d}{dx}\int\limits\limits\limits_{0}^{0}\sin(\sqrt{t^{2}+\pi^2})\;dt = 0\] (since the area from 0 to 0 is zero) So since b=0 it'll be y = mx

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.1Looks like m=0 too, since \[\large m = \sin(\sqrt{0^{2}+\pi^2}) = \sin \sqrt {\pi^2} = \sin \pi = 0\] so y=0
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.