Babynini
  • Babynini
Limits....again. Help!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Babynini
  • Babynini
Both numbers 6 and 7, but let's begin with 6!!
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Babynini
  • Babynini
@peachpi @zepdrix :)
Astrophysics
  • Astrophysics
L'hospital for first one

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Babynini
  • Babynini
#6) b = 4?
zepdrix
  • zepdrix
Ya :) Imma wait and see what Ganeshie has to say though ^^
ganeshie8
  • ganeshie8
Notice that the denominator is 0 when you plugin x=0 Also, for the limit to exist (finite), you must get the indeterminate 0/0 form when you plugin x=0. otherwise the limit does not exist (infinite). so, the numerator part must evaluate to 0 at x=0
ganeshie8
  • ganeshie8
\(\sqrt{ax+b}-2\) evaluating it at \(x=0\) and setting equal to \(0\) does give you \(b=4\)
ganeshie8
  • ganeshie8
plugin the \(b\) value, rationalize and you will see what \(a\) needs to be
Astrophysics
  • Astrophysics
For 7 note this |dw:1444533414414:dw| you can do the same with |2x-1| you'll have an ugly numerator at the beginning, but it'll simplify to something nice :D
Babynini
  • Babynini
Right, so I got b. But the a is being something terrible.
ganeshie8
  • ganeshie8
\[\frac{\sqrt{ax+4}-2}{x}=\frac{ax+4-4}{x(\sqrt{ax+4}+2)} = \frac{a}{\sqrt{ax+4}+2}\] plugin x=0 and you will see immediately that \(a\) needs to be \(4\)
dan815
  • dan815
|dw:1444533867422:dw|
Babynini
  • Babynini
@ganeshie8 thanks! I got it :)
Babynini
  • Babynini
@dan815 gwow you are doing some fancy stuff, I think I also follow wht you are doing :D
Babynini
  • Babynini
mm well if a = 4 and b = 4..then it works.
Babynini
  • Babynini
but it's always over 0 :/
Astrophysics
  • Astrophysics
a should be 4
Babynini
  • Babynini
Ok, yeah that's what I got xD thanks yall :)
dan815
  • dan815
you actully do get a limit!
dan815
  • dan815
|dw:1444534732654:dw|
dan815
  • dan815
okay i hope thats clear now
dan815
  • dan815
i think this is how lhopital is justified too
dan815
  • dan815
we are looking at the behavior of your function very locally, so we'd only care about the slopes changes around that point
Babynini
  • Babynini
Righto, 6 all makes sense :) I'm going to start a new thread for number 7
dan815
  • dan815
so for example the lhopital way d/x(abs(2x-1)- abs(2x+)) --------------------- d/dx(x) d/dx ( abs(2x-1) - d/dx(abs(2x+1)) ------------------------------- 1 now derivative of abs(2x-1) near 0 = is -2 and the detiaive of abs(2x+1) near 0 is 2 so -2 - 2 ------- 1 =-4 as x-->0
Babynini
  • Babynini
Em, haven't learnt derivatives yet :/
dan815
  • dan815
okay then do it the other way
Astrophysics
  • Astrophysics
I think multiplying by conjugate might work
dan815
  • dan815
yeah

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