anonymous
  • anonymous
Compute lim x->0 (4x/sin(3x)+x/cos(3x))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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myininaya
  • myininaya
\[\lim_{x \rightarrow 0}(\frac{4x}{\sin(3x)}+\frac{x}{\cos(3x)}=\frac{4}{3}\lim_{x \rightarrow 0}\frac{3x}{\sin(3x)}+\lim_{x \rightarrow 0}\frac{x}{\cos(3x)}\] Recall \[\lim_{u \rightarrow 0}\frac{u}{\sin(u)}=1\]
myininaya
  • myininaya
the other one is just direct sub.
anonymous
  • anonymous
i didnt quite understand what you just showed =/

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myininaya
  • myininaya
Nothing?
anonymous
  • anonymous
okay so what did you do their when you put 4/3
myininaya
  • myininaya
4/3 * 3 =4 I just multiplied the first fraction by 3/3
anonymous
  • anonymous
which became 12x/sin(9x)?
myininaya
  • myininaya
oh no
myininaya
  • myininaya
3sin(3x) does not equal sin(9x)
anonymous
  • anonymous
oh ur right lol sorry about that
anonymous
  • anonymous
whats the purpose of multiplying by 3/3?
myininaya
  • myininaya
\[\lim_{u \rightarrow 0}\frac{u}{\sin(u)}=1\] Do you recall this?
anonymous
  • anonymous
i dont
myininaya
  • myininaya
so this means we can say \[\lim_{x \rightarrow 0}\frac{3x}{\sin(3x)}=1\]
anonymous
  • anonymous
alright
myininaya
  • myininaya
so I wanted a 3 up there in our problem
myininaya
  • myininaya
but if i put a 3 on top I have to put a 3 on bottom
anonymous
  • anonymous
yes
myininaya
  • myininaya
so that is why I multiplied by 3/3
anonymous
  • anonymous
i get it so the first part became 1
myininaya
  • myininaya
yes 4/3 times 1 is the first part
myininaya
  • myininaya
not the second part we just plug in 0
myininaya
  • myininaya
now*
myininaya
  • myininaya
is everything ok? you got it?
anonymous
  • anonymous
im writing it down
myininaya
  • myininaya
ok
anonymous
  • anonymous
so then it would be 0/cos(3(0))
myininaya
  • myininaya
0/1=0
myininaya
  • myininaya
yes
myininaya
  • myininaya
so we have 4/3 from the first part+ 0 from the second part =4/3
anonymous
  • anonymous
oh got it thanks!
myininaya
  • myininaya
:)
myininaya
  • myininaya
Spikey I appreciate that you want to learn this stuff. Thanks for engaging in the learning process. That is really cool dude.
anonymous
  • anonymous
lol thank you :) i take AP calc
anonymous
  • anonymous
in highschool
myininaya
  • myininaya
Go you! :)
myininaya
  • myininaya
It is really cool to have that attitude. You will go far.
anonymous
  • anonymous
theres just some stuff that i dont really comprehend my teacher doesnt teach some stuff clearly
anonymous
  • anonymous
lol yeah i never give up. :)
anonymous
  • anonymous
always trying to learn new things.
myininaya
  • myininaya
Good luck to you and peace out!
anonymous
  • anonymous
lol bye

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