anonymous
  • anonymous
I got a doubt in limits see below for my question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[\lim_{x \rightarrow 0}\]\[sinax / tanbx\]
anonymous
  • anonymous
its 0/0 form
anonymous
  • anonymous
This is the actual question \[\lim_{x \rightarrow 0} sinax/tanbx\]

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anonymous
  • anonymous
differentiate top and bottom acos(ax) / b sec^2 (bx)
anonymous
  • anonymous
sub x=0
anonymous
  • anonymous
answer = (a/b)
anonymous
  • anonymous
multiply and divide by bx/ax
anonymous
  • anonymous
I don't know differntiation and u mean that i should multiply the numerator by ax/ax and denominator by bx/bx????
anonymous
  • anonymous
I dont even know what him was on bout either lol
anonymous
  • anonymous
if you havent done derivatives then your teacher shouldnt be giving you this question !
anonymous
  • anonymous
this can be done without derivatives
anonymous
  • anonymous
that's wat i am saying him1618 you are right
anonymous
  • anonymous
how? , and its much easier with derivatives, 2lines of work
anonymous
  • anonymous
its not pinching theorm
anonymous
  • anonymous
yeah its easier..no doubt 110 times out of 100 id use derivatives, but the fact is that if hes doing limits fundamentally its imperative for him to know the fundamental steps..rather than shortcuts
anonymous
  • anonymous
so i guess he wants a legitimate fundamental method which uses standard limit definitions
anonymous
  • anonymous
exactly now can u pls explain
anonymous
  • anonymous
first divide above and below by x
anonymous
  • anonymous
then make a form like this \[[\sin( ax )/ax] /[\tan (bx)/bx] \] x a/b
anonymous
  • anonymous
the book i am goin through says multiply the numerator by ax/ax and the denominator by bx/bx
anonymous
  • anonymous
yeah thats right..dont look at the solns..which book is this?
anonymous
  • anonymous
u understood wt i did?
anonymous
  • anonymous
nope the book is my coaching book
anonymous
  • anonymous
i did not understand wat wud happen if i divided by x????
anonymous
  • anonymous
its the same thing
anonymous
  • anonymous
ok divide sin ax by ax and tan bx by bx
anonymous
  • anonymous
and then you will have to multiply by a/b also, to keep it the same..understand?
anonymous
  • anonymous
so sinax by ax, with x tending to zero is 1, and so is tanbx by bx so the ans is 1 x a/b a/b
anonymous
  • anonymous
samjha?
anonymous
  • anonymous
yeh I remember that way , just the way the question looked put me off lol
anonymous
  • anonymous
also, I just differentiate top and bottom etc, its so easy and there no brain required
anonymous
  • anonymous
yeah everyone does that..me too.bt the kid wanted a method...i know no one in the world would not use derivatives for this..even the kid will start using em after a couple of months
anonymous
  • anonymous
ok ab question yeh hai ki jo ax aur bx hum multiply aur divide karte hain woh idhar kya kar rahen hai???
anonymous
  • anonymous
tujhe pata hai sinx / x is 1 when x tends to zero
anonymous
  • anonymous
how do i k now dat is it a rule or smthing??
anonymous
  • anonymous
its the first rule you learn in limits
anonymous
  • anonymous
let me check
anonymous
  • anonymous
sinx / x =1 and tanx / x is 1 when x tends to zero
anonymous
  • anonymous
k yes got it!!!!!!
anonymous
  • anonymous
so now if you have sin kx /x with x tending to zero and k any integer, whts the limit
anonymous
  • anonymous
is it ax/bx??
anonymous
  • anonymous
sin kx / x with x tending to zero??answer kya hai?
anonymous
  • anonymous
1
anonymous
  • anonymous
no its k
anonymous
  • anonymous
multiply and divide by k
anonymous
  • anonymous
yeah its k sorry yaar!!!!!!
anonymous
  • anonymous
so in the same way u treat ur question as two different limits and then take their ratio...
anonymous
  • anonymous
but if we do dis we get \[\sin ax/ax * ax = 1*ax = ax\]
anonymous
  • anonymous
but then u have bx below..cancel x..u get a/b
anonymous
  • anonymous
can i cancel (sin ax)/ax ka x???? to get a i don't think so!!!!
anonymous
  • anonymous
vaise u cant..but when uve got b in the denominator u can
anonymous
  • anonymous
how and y can i do dat??? any spl reason behind it???
anonymous
  • anonymous
abe...............sinax / ax / tanbx / bx x a/b
anonymous
  • anonymous
is it the same as sinax/tanbx
anonymous
  • anonymous
yups
anonymous
  • anonymous
to evaluate sinax/tanbx u need to form sinax/ ax/tanbx/bx....to make the expression same uve got to multiply by a/b
anonymous
  • anonymous
luks like i got it the sin x / x = 1 wala way!!!!!!
anonymous
  • anonymous
i got ax / bx where i can cancel x
anonymous
  • anonymous
is this tareeka ok!!!!!!!!!
anonymous
  • anonymous
sin ax / tan bx = sin(ax) x ax --------- ax ---------- tan (bx) x bx --------- bx
anonymous
  • anonymous
theek hai?
anonymous
  • anonymous
is the ax between the 2 xes for multiplying
anonymous
  • anonymous
abe that x is multiply
anonymous
  • anonymous
if so tab theek hai got it!!!!!!
anonymous
  • anonymous
thanx got it!!!!!!!!

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