Question

find lim h->0 [sin(6x+6h)-sin(6x)/h]

Answer 1

hey ,is this the original q ?

Answer 2

Yes

Answer 3

is everything \[\frac{\sin(6x+6h)-\sin6x }{ h }\]
like this?

Answer 4

yes

Answer 5

Wow, that matches the definition of a derivative.

Answer 6

Have you been taught derivatives or do you have to compute this limit without any help of those?

Answer 7

THE DEFINATION OF THE DERIVATIVE???? DO U KNOW IT?

Answer 8

yes but i was taught it a while ago and dont remember how to solve it. I know derivatives.

Answer 9

yeah, the question like to find the derivative of y = sin(6x)

Answer 10

OK, so this is the definition of the derivative of sin(6x). Do you know the Chain Rule?

Answer 11

yes for sin(6x) it would be cos(6x) (6)

Answer 12

Wonderful! 6cos(6x) should be enough.

Answer 13

but maybe the question requires the use of limit definition to find the answer.

Answer 14

Hmm, but if he was taught derivatives, then why take the longer route?

Answer 15

why go to derivative definition when the question specifically ask for the limit.
(the only reason can be that the question itself belongs to derivative topic)

Answer 16

so ej, does this belong to derivative topic or limit ?

Answer 17

OP knows what a derivative is. That should be enough for him.

Answer 18

ok, if ej doesn't mind, then i'm ok too :)

Answer 19

Err, sorry... I might have appeared downright rude there

Answer 20

It is a multiple choice questions the answer options are a.) 0 b.) 6sin(6x) c.)6cos(6x) d.) -6cos(6x) e.)-6sin(6x)

Answer 21

i need to show work though

Answer 22

Then our work is correct.

Answer 23

how do I get rid of h in the denominator

Answer 24

Even though I know the easy way to solve this i have to show the long way with work to get full credit.

Answer 25

Do you want to do it with the definition of a limit?

Answer 26

solving using the definition of derivative is what it is asking

Answer 27

Then we have done it. The definition of a derivative is lim h->0 [f(x+h)-f(x)]/h
Here, f(x) is sin(6x)