Question

evaluate the following apply limit
lim
theta->0
sin(under root 2theta)/(underroot2theta)

Answer 1

hope u can undrstand the question

Answer 2

1

Answer 3

i need the solution

Answer 4

:(

Answer 5

\[\lim_{\theta \rightarrow 0} \sin \sqrt{\theta}\div \sqrt{\theta}=1\]

Answer 6

let sqrt(2theta)=t
then u get sint / t
t ->0

Answer 7

lim X-->0 of sinx/x=1 tht's smth tht is given and u have to remember ...

Answer 8

1 is the limit

Answer 9

what you need to know to do this is that
\[lim_{x->0}\frac{sin(x)}{x}=1\]

Answer 10

of course that limit is no different than
\[lim_{x->0}\frac{sin(2x)}{2x}=1\]

Answer 11

and the square root of one is one.

Answer 12

then again maybe it was
\[lim_{x->0} \frac{sin(\sqrt{x})}{\sqrt{x}}\] which is of course the same

Answer 13

or even
\[lim_{x->0}\frac{sin(2\sqrt{x})}{2\sqrt{x}}\]

Answer 14

are you convinced of this or no?

Answer 15

No1 would have explained it better :):)
G j Satellite :):)

Answer 16

you know now that i think about it maybe this is a trick

Answer 17

and you are supposed to say that the limit does not exist

Answer 18

because the domain of thing beast is
\[x\geq 0\] and therefore you cannot approach 0 from the left

Answer 19

now that i think of it...i think satellites right

Answer 20

so perhaps that was the point of this question

Answer 21

W8.....explain me again plsss

Answer 22

the lhl wouldnt exist

Answer 23

see the right hand limit is 1, and that part is fine

Answer 24

unless it says\[lim_{x->0^+}\frac{sin(\sqrt{x})}{\sqrt{x}}\]

Answer 25

oh..i got it!!

Answer 26

but from the left side, if u put 0-h for theta, ud get the root of a negative number, which doesnt exist, for real

Answer 27

cannot take a limit because the function does not exist to the left. on account of the square root.

Answer 28

what him1618 said

Answer 29

satellite keeps on proving how amazing he is

Answer 30

yeah right

Answer 31

but i will thank you for the compliment

Answer 32

Yea.yea.....u 2 r right....Thnx :)
(Satellite is a he?) oO

Answer 33

does it say limit from the left or just limit?

Answer 34

r u a he satellite?

Answer 35

i'll never tell

Answer 36

I've always thought he/she is a she...

Answer 37

beauty of the world wide interweb is you can be anyone. a dog even

Answer 38

im sure its a she....

Answer 39

I'm pretty sure is a she too :P so whtever ur....for us ur a she :P

Answer 40

amazing then..some gorgeous lady supporting a 180 iq

Answer 41

whose IQ is 180? urs?

Answer 42

hehe thanx every 1
satellite,him1618 and angela:)
thanx a lot

Answer 43

satellites i think..lol..m talkin abt her

Answer 44

welcome mimi

Answer 45

Haha lol :P:P :)
uw :)

Answer 46

:)

Answer 47

btw angela i first fell in love on 21st july...:)

Answer 48

:)

Answer 49

wht year?

Answer 50

2007

Answer 51

we were still 14 then...

Answer 52

u remember the date? Interesting...I probably wouldn't :P:P

Answer 53

i remember a lot...lol...no use though..no response....

Answer 54

I remember only dates tht have to do with history lessons :P:P
And I'm sorry :S

Answer 55

sweet of u...i never remembered history..except perhaps the knights templar and stuff...

Answer 56

I remember dates such as when was Magna Carta was signed,or when did the Roman Empire split in 2...these things :P..nothing abt albanian history though,...only independence day :P:P

Answer 57

hahaha....

Answer 58

:D:D ^_^

Answer 59

Here is a great little visualization and explanation of the basic limit \(\lim_{x\to 0}\frac{\sin(x)}{x}\). http://www.ies.co.jp/math/java/calc/LimSinX/LimSinX.html

Hope this helps. :)