Question

another limit question.

Answer 1

\[\lim_{ \theta \rightarrow 0}\frac{ \sin 3\theta }{ \theta^2 }\]

Answer 2

seriously, no examples from the book explains most of the problems. argg

Answer 3

you know what sin x/x when x->0 us ?

Answer 4

**is ?

Answer 5

yeah, it equals 1

Answer 6

so , will be
lim 3theta -> 0 sin (3theta)/ 3theta = 1
right ?
i just put x= 3 theta

Answer 7

oh, arent u just restating hte question then, the limit can't be 1 can it?

Answer 8

the*

Answer 9

i haven't yet started solving it ... :P

i did that because i am gonna use this :
lim 3theta -> 0 sin (3theta)/ 3theta = 1

Answer 10

now in your Q, we have lim theta -> 0

so 3theta will also tend to 0, got this?

Answer 11

uh, yeah, i basically what i did was just plug in theta to 0 and i got stuck cuz i dunno what sin 0 / 0 is.

Answer 12

thats 0/0 indeterminate form, thats why we use the formula sin x/x =1

Answer 13

now

lim 3theta-> 0 sin 3theta / theta^2

= lim 3theta-> 0 (sin 3theta / theta) / theta

got this important step ?

Answer 14

lim 3theta-> 0 sin 3theta / theta^2

= lim 3theta-> 0 (sin 3theta / theta) / theta

=lim 3theta-> 0 3* (sin 3theta / 3theta) / theta
(multiplied and divided by 3 to get the form of sin 3theta/ 3theta)
= 3 * [lim 3theta-> 0 (sin 3theta / 3theta) ] / [lim theta-> 0 theta ]

=3* [1]/ [0] = infinity