Question

lim t → 0 sin 9t/8t

Answer 1

lim sin(x)/x is 1

write the bottom 8t as 8/9 * 9t (which is still 8t)
that turns the problem into
9/8 * sin(9t)/(9t)

Answer 2

i gont got it

Answer 3

?

Answer 4

dont

Answer 5

do you know
lim x->0 sin(x)/x = 1
?

Answer 6

i know

Answer 7

lim t->0 sin(9t)/(9t)

is the same problem... let x = 9t
as t->0 9t->0 which means x-> 0
and we have the problem
lim x->0 sin(x)/x
which we know is 1

does that part make sense?

Answer 8

yes

Answer 9

next what is the limit of
lim x->0 (9/8) sin(x)/x ?
we can factor the 9/8 out and do
(9/8) lim x->0 sin(x)/x
which is
9/8 * 1 = 9/8

does that make sense ?

Answer 10

yes

Answer 11

we can re-write
(9/8) sin(x)/x
as
sin(x) / (8x/9)

agreed ?

Answer 12

multiply top and bottom by 8/9 to change
(9/8) sin(x)/x into sin(x) / (8x/9)

Answer 13

Here it is in a bigger font

Answer 14

i got it

Answer 15

now if we replace x with x= 9t
this becomes (see attached)

Answer 16

The idea is to change the original problem into a sin(x)/x because we know how to find the limit of that.

Answer 17

sin/8

Answer 18

the answer is 9/8

Answer 19

oky