Question

I got a doubt in limits see below for my question

Answer 1

\[\lim_{x \rightarrow 0}\]\[sinax / tanbx\]

Answer 2

its 0/0 form

Answer 3

This is the actual question \[\lim_{x \rightarrow 0} sinax/tanbx\]

Answer 4

differentiate top and bottom acos(ax) / b sec^2 (bx)

Answer 5

sub x=0

Answer 6

answer = (a/b)

Answer 7

multiply and divide by bx/ax

Answer 8

I don't know differntiation and u mean that i should multiply the numerator by ax/ax and denominator by bx/bx????

Answer 9

I dont even know what him was on bout either lol

Answer 10

if you havent done derivatives then your teacher shouldnt be giving you this question !

Answer 11

this can be done without derivatives

Answer 12

that's wat i am saying him1618 you are right

Answer 13

how? , and its much easier with derivatives, 2lines of work

Answer 14

its not pinching theorm

Answer 15

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

Answer 16

so i guess he wants a legitimate fundamental method which uses standard limit definitions

Answer 17

exactly now can u pls explain

Answer 18

first divide above and below by x

Answer 19

then make a form like this
\[[\sin( ax )/ax] /[\tan (bx)/bx] \] x a/b

Answer 20

the book i am goin through says multiply the numerator by ax/ax and the denominator by bx/bx

Answer 21

yeah thats right..dont look at the solns..which book is this?

Answer 22

u understood wt i did?

Answer 23

nope the book is my coaching book

Answer 24

i did not understand wat wud happen if i divided by x????

Answer 25

its the same thing

Answer 26

ok divide sin ax by ax and tan bx by bx

Answer 27

and then you will have to multiply by a/b also, to keep it the same..understand?

Answer 28

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

Answer 29

samjha?

Answer 30

yeh I remember that way , just the way the question looked put me off lol

Answer 31

also, I just differentiate top and bottom etc, its so easy and there no brain required

Answer 32

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

Answer 33

ok ab question yeh hai ki jo ax aur bx hum multiply aur divide karte hain woh idhar kya kar rahen hai???

Answer 34

tujhe pata hai sinx / x is 1 when x tends to zero

Answer 35

how do i k now dat is it a rule or smthing??

Answer 36

its the first rule you learn in limits

Answer 37

let me check

Answer 38

sinx / x =1 and tanx / x is 1 when x tends to zero

Answer 39

k yes got it!!!!!!

Answer 40

so now if you have sin kx /x with x tending to zero and k any integer, whts the limit

Answer 41

is it ax/bx??

Answer 42

sin kx / x with x tending to zero??answer kya hai?

Answer 43

1

Answer 44

no its k

Answer 45

multiply and divide by k

Answer 46

yeah its k sorry yaar!!!!!!

Answer 47

so in the same way u treat ur question as two different limits and then take their ratio...

Answer 48

but if we do dis we get \[\sin ax/ax * ax = 1*ax = ax\]

Answer 49

but then u have bx below..cancel x..u get a/b

Answer 50

can i cancel (sin ax)/ax ka x???? to get a i don't think so!!!!

Answer 51

vaise u cant..but when uve got b in the denominator u can

Answer 52

how and y can i do dat??? any spl reason behind it???

Answer 53

abe...............sinax / ax / tanbx / bx x a/b

Answer 54

is it the same as sinax/tanbx

Answer 55

yups

Answer 56

to evaluate sinax/tanbx u need to form sinax/ ax/tanbx/bx....to make the expression same uve got to multiply by a/b

Answer 57

luks like i got it the sin x / x = 1 wala way!!!!!!

Answer 58

i got ax / bx where i can cancel x

Answer 59

is this tareeka ok!!!!!!!!!

Answer 60

sin ax / tan bx = sin(ax) x ax
---------
ax
----------
tan (bx) x bx
---------
bx

Answer 61

theek hai?

Answer 62

is the ax between the 2 xes for multiplying

Answer 63

abe that x is multiply

Answer 64

if so tab theek hai got it!!!!!!

Answer 65

thanx got it!!!!!!!!