Mathematics
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OpenStudy (anonymous):
lim x->-infinti of sqrt (3x^2+6) / 5-2x
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OpenStudy (anonymous):
\[\lim_{x \rightarrow -\infty} \sqrt{3x ^{2+6}} \div 5-2x\]
OpenStudy (anonymous):
\[\frac{\sqrt{3}}{2}\]
myininaya (myininaya):
\[\frac{\sqrt{3x^2+6}}{5-2x}\]
OpenStudy (anonymous):
with your eyeballs
OpenStudy (anonymous):
so sqrt3/-2?
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OpenStudy (anonymous):
no because you are going to
\[-\infty\] yes?
myininaya (myininaya):
\[\frac{\sqrt{3x^2+6}}{5-2x}*\frac{\frac{1}{x}}{\frac{1}{x}}\]
=\[\frac{\sqrt{\frac{3x^2}{x}+\frac{6}{x}}}{{\frac{5}{x}-\frac{2x}{x}}}\]
OpenStudy (anonymous):
if you were going to
\[\infty\] you would be right. but you are going to
\[-\infty\] so both top and bottom are positive
OpenStudy (anonymous):
??
myininaya (myininaya):
\[\frac{\sqrt{3x+\frac{6}{x}}}{\frac{5}{x}-2}\]
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OpenStudy (anonymous):
ohh..so its - infinit?
myininaya (myininaya):
right it goes to -inf
OpenStudy (anonymous):
dunno but that looks like what you wrote yes?
OpenStudy (anonymous):
lim x->-infinti of sqrt (3x^2+6) / 5-2x
OpenStudy (anonymous):
i think so?
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myininaya (myininaya):
of x->-inf didn't see the negative
OpenStudy (anonymous):
ok in that case it is
\[\frac{\sqrt{3}}{2}\] fer sure
myininaya (myininaya):
i don't agree
OpenStudy (anonymous):
hello myininaya!
myininaya (myininaya):
oops i do agree
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OpenStudy (anonymous):
well you are probably right and i am wrong as usual
OpenStudy (anonymous):
lol so step by step..the powers dont match..so i thought it wud jus b 0 or doesnt exisit?
OpenStudy (anonymous):
oh then if you agree i disagree! lol
myininaya (myininaya):
i divided top by wrong thing
it is suppose to be sqrt(x^2)
OpenStudy (anonymous):
forget that noise (no offence)
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myininaya (myininaya):
i will write this out again in prettiness okay
OpenStudy (anonymous):
okay:)
OpenStudy (anonymous):
look. denominator is poly of degree 1 yes? numerator is not a poly but for limit purposes it might as well be. nothing matter but highest degree
OpenStudy (anonymous):
forget everything after the
\[\sqrt{3x^2}=\sqrt{3}x\]
myininaya (myininaya):
\[\frac{\sqrt{3x^2+6}}{5-2x}*\frac{\frac{1}{x}}{\frac{1}{x}}=\frac{\sqrt{\frac{3x^2+6}{x^2}}}{\frac{5}{x}-\frac{2x}{x}}\]
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OpenStudy (anonymous):
so you get
\[\frac{\sqrt{3}x}{-2x}=\frac{\sqrt{3}}{-2}\]
myininaya (myininaya):
\[\frac{\sqrt{3+\frac{6}{x^2}}}{\frac{5}{x}-2}\]
OpenStudy (anonymous):
not that my esteemed colleague is wrong, it is just that you can do this with your eyes
myininaya (myininaya):
6/x^2->0
5/x->0
OpenStudy (anonymous):
but isnt it \[\sqrt{3x ^{2}}\]
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OpenStudy (anonymous):
anyway i should be quiet because myininaya is way smarter than i am
OpenStudy (anonymous):
right and
\[\sqrt{3x^2}=\sqrt{3}x\]\]
OpenStudy (anonymous):
what about the power to 2?
myininaya (myininaya):
not true satellite
OpenStudy (anonymous):
\[\sqrt{x^2}=|x|\]
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OpenStudy (anonymous):
what is not true?
myininaya (myininaya):
since x->-inf, f(x)->sqrt{3}/2
if x->inf, f(x)->-sqrt{3}/2
that im smater (its not true)
OpenStudy (anonymous):
way smarter
OpenStudy (anonymous):
both of u r smart! im not
OpenStudy (anonymous):
but i did cross the 1000 mark! no one threw a party :(
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myininaya (myininaya):
i threw a party for you and i forgot to invite you sorry
OpenStudy (anonymous):
!!! no bike rides for you!
OpenStudy (anonymous):
since x->-inf, f(x)->-sqrt{3}/2
if x->inf, f(x)->sqrt{3}/2
i thought it was this?
myininaya (myininaya):
then you thought correctly!
OpenStudy (anonymous):
didnt u say the opp of tht previosuly?
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OpenStudy (anonymous):
you have a - sign in the denominator. so no sorry
myininaya (myininaya):
oops i didn't see you change the signs sorry
OpenStudy (anonymous):
ohh right..4got abt tht negative
OpenStudy (anonymous):
denominator is 5 - 2x so as x -> infinity this goes to - infinity and vice versa
myininaya (myininaya):
if x is negative and there is a negative sign in front of it that number would be positive right?
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OpenStudy (anonymous):
so the ans is -3/2?
OpenStudy (anonymous):
i am taking my 1005 medals and going to bed.
no
\[\frac{\sqrt{3}}{2}\]
OpenStudy (anonymous):
ohhok...i think i got it
OpenStudy (anonymous):
good. don't forget the coefficient in the numerator is
\[\sqrt{3}\] not 3
OpenStudy (anonymous):
alrigty:) thanks a ton!
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OpenStudy (anonymous):
yw
myininaya (myininaya):
sanhitha you forgot to ask him if he is indian
im disappointed in you
myininaya (myininaya):
jk
OpenStudy (anonymous):
lol..dude! i only asked 2 ppl includin u
OpenStudy (anonymous):
haha
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OpenStudy (anonymous):
haha thts funny
OpenStudy (anonymous):
woof