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anonymous
 one year ago
f''(x)=2+cosx, f(0)=10, f(pi/2)=1 is the last one that I am stuck on. Find f @jhannybean @freckles @FireKat97
anonymous
 one year ago
f''(x)=2+cosx, f(0)=10, f(pi/2)=1 is the last one that I am stuck on. Find f @jhannybean @freckles @FireKat97

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let's integrate f''(x). what did you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f'(x) = \int f''(x)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0_ im a little off today altogether, lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f'(x) = 2x+\sin(x)\]\[f(x) = \int f'(x) = ~?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Great. Now we take care of our conditions.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x) = x^2\cos(x) + Cx + D\] Don't forget that you add on a constant every time you integrate.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right I know I'm not sure why I left it off lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So if \(f(0) =10\) then we're basically finding our D value. \[10=(0)^2\cos(0)+C(0) +D\qquad \implies D=~?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Tell me how you got 9.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no never mind its 11

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you mind rewriting the whole problem out again please with d replaced with 11

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i believe you're using equation mode but I'm not sure if i operate it correctly lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x)=x^2\cos(x)+Cx+11\] And now we take care of our second condition. \(f\left(\dfrac{\pi}{2}\right) = 1\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So \[1=\left(\frac{\pi}{2}\right)^2  cos\left(\frac{\pi}{2}\right) +\frac{\pi}{2}C +11\]Solve for C.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I wouldn't bother simplifying anything but isolating C first. Then you can simplify allyou want.Makes thigns a lot easier

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so far i got \[(10\pi/4)/(\pi/2)\]=C

freckles
 one year ago
Best ResponseYou've already chosen the best response.0(pi/2)^2=pi^2/4 not pi/4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yes that is true i forgot to add that in lo i had t on my paper but didnt type it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[1\left(\frac{\pi}{2}\right)^2 +\cos\left(\frac{\pi}{2}\right) 11=\frac{\pi}{2}C\]Simplify the LHS \[1\frac{\pi^2}{4}11 = \frac{\pi}{2}C\]\[\frac{4\pi^244}{4}=\frac{\pi}{2}C\]\[\frac{40\pi^2}{4}\cdot \frac{2}{\pi}=C\]\[C= \frac{40\pi^2}{2\pi} =\frac{20}{\pi} \frac{\pi}{2} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Are you able to follow that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the answer should be \[x^2\cos(x)20/\pi\pi/2+11\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\therefore \qquad f(x) = x^2\cos(x)+\left(\frac{20}{\pi}\frac{\pi}{2}\right)x +11\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0damn i forgot the x and it said it was wrong i guess I'm getting tired lol well thank you for all your help !
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