arianna1453
  • arianna1453
Hey I need help with some calculus questions. (:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
arianna1453
  • arianna1453
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J.Maule
  • J.Maule
ask @Michele_Laino he can prob help
jango_IN_DTOWN
  • jango_IN_DTOWN
hii

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arianna1453
  • arianna1453
Hey can you help me?
jango_IN_DTOWN
  • jango_IN_DTOWN
Yes
arianna1453
  • arianna1453
I already found the derivatives of each function. I just dont understand how to find the domain.
jango_IN_DTOWN
  • jango_IN_DTOWN
when x<4, f(x)=5x-6 whose derivative is 5 when 4<=x<=6 f(x)=x^2-2 whose derivative is 2x when x>6, f(x)=4x+10 whose derivative is 4
jango_IN_DTOWN
  • jango_IN_DTOWN
now we have to check the domain
arianna1453
  • arianna1453
Yes, I got that part (:
jango_IN_DTOWN
  • jango_IN_DTOWN
f'(4)=2.4=8 which is not equal to the Lf'(4)
arianna1453
  • arianna1453
Wait. how did you do that.
jango_IN_DTOWN
  • jango_IN_DTOWN
f'(6)=2.6=12 and Rf'(6)=4 so f is not derivable at x=6
jango_IN_DTOWN
  • jango_IN_DTOWN
for existence of derivative we must have Lf'(x)=Rf'(x)
arianna1453
  • arianna1453
Okay, I am still a little confused on that part, so the domain is that x cannot equal 4 and 6
jango_IN_DTOWN
  • jango_IN_DTOWN
wait
arianna1453
  • arianna1453
Well all real numbers but 4 and 6
jango_IN_DTOWN
  • jango_IN_DTOWN
no no let me write the answer f'(x)=5, when x<4 f'(x)=2x, when 46
arianna1453
  • arianna1453
Ohhhhh okay. I see now.
jango_IN_DTOWN
  • jango_IN_DTOWN
yeah the domain is all real numbers except 4 and 6
arianna1453
  • arianna1453
Thank you. That makes sense!
arianna1453
  • arianna1453
Would you mind trying to help me with another question?
jango_IN_DTOWN
  • jango_IN_DTOWN
ok
arianna1453
  • arianna1453
Getting stuck on this one
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jango_IN_DTOWN
  • jango_IN_DTOWN
multiply numerator and denominator by 1+cos x
jango_IN_DTOWN
  • jango_IN_DTOWN
so \[y=\frac{ (1+\cos x)^2 }{ 1-\cos ^2 x}=\frac{ 1+\cos ^2 x +2 \cos x }{ \sin ^2 x }\]
jango_IN_DTOWN
  • jango_IN_DTOWN
wait you may directly differentiate
arianna1453
  • arianna1453
See, the answer choices are confusing me. I cant figure out how to get one of those.
1 Attachment
jango_IN_DTOWN
  • jango_IN_DTOWN
\[\frac{ d }{ dx}(\frac{ f(x) }{ g(x) })=\frac{ g(x)f'(x)-f(x)g'(x) }{ {g(x)}^2 }\]
jango_IN_DTOWN
  • jango_IN_DTOWN
@arianna1453
arianna1453
  • arianna1453
oh okey.
jango_IN_DTOWN
  • jango_IN_DTOWN
use the formula and tell me the answer
jango_IN_DTOWN
  • jango_IN_DTOWN
@arianna1453 option d is correct
arianna1453
  • arianna1453
Give me a second. Working it out.
arianna1453
  • arianna1453
are you sure its d @jango_IN_DTOWN ?
jango_IN_DTOWN
  • jango_IN_DTOWN
yeah you want me to work it out?
arianna1453
  • arianna1453
Yeah, if you could.
jango_IN_DTOWN
  • jango_IN_DTOWN
\[f'(x)=\frac{ (1-\cos x)(-\sin x)-(1+\cos x) \sin x }{ (1-\cos x)^2 }\]
jango_IN_DTOWN
  • jango_IN_DTOWN
\[=\frac{ -\sin x +\sin xcos x-\sin x -\sin x \cos x }{ (1-\cos x)^2 }\]
jango_IN_DTOWN
  • jango_IN_DTOWN
\[=\frac{ -2\sin x }{ (1-\cos x)^2 }\]
arianna1453
  • arianna1453
OH. I had one of my signs wrong. I got it!! Thank you
jango_IN_DTOWN
  • jango_IN_DTOWN
n.p.
arianna1453
  • arianna1453
Last one i will ask you. Is this one correct?
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arianna1453
  • arianna1453
@jango_IN_DTOWN ?
jango_IN_DTOWN
  • jango_IN_DTOWN
option c is correct

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