Question

lim x->0 sin(3x)/3x^(2)+x, can someone help?

Answer 1

Plug the limit into the equation first to see if you get a real answer. If not (which happens), use L'Hopital's Rule: find the derivative of the numerator and denominator, that becomes the new "equation." Plug in the limit, see if you get a real answer.

Answer 2

In my head, I got an answer, I'll see if you got it.

Answer 3

k let me try

Answer 4

is it 0?

Answer 5

No, when you plug in the limit at first glance, you'll get 0/0, which is an indeterminate form of a limit. Now take the derivative of the top, the derivative of the bottom, and plug in 0 again.

Answer 6

thats what i did

Answer 7

Hmm, what did you get for the "new" equation

Answer 8

3cos3x/6x+1 , if u plug zero u get o

Answer 9

Nope, look again. ;)

Answer 10

wait hold on i am coming home , its actually 0/1 , rght?

Answer 11

No, that would still be 0. [3*cos(0)]/[0+1]

Answer 12

its hard to leave this things aloneee, yeaaa i was wondering the same thing

Answer 13

Hint: cos(0) is 1.

Answer 14

waaaaaa still dont get it

Answer 15

It's hard to do these things alone

Answer 16

:o So we have the limit as x approaches 0 of [(3cosx)/(6x+1)]. If we plug in 0, we'll get (3*1)/(0+1) Now you see? I'm not giving the true final answer lol.

Answer 17

its 3cos3x right?

Answer 18

not 3cosx

Answer 19

Oh sorry, 3*cos3x. But if we plug in 0, we'll still get 3*cos0, which is still 3*1 = 3.

Answer 20

so 3 right ?

Answer 21

Right, final answer will be 3/1 = 3. Not 0.

Answer 22

could u helo me here like lets says tanx=1 , how would i look at the unit circle for it ?

Answer 23

Err, tanx = 1, to solve for x, you would need the special triangle.

Answer 24

It's just a special case. If you remember, the tangent of an angle is opposite/adjacent. The tangent of a 45 degree angle, as seen in the pic, is 1/1 = 1.

Answer 25

like here is my question and in the end i get , cosx=0 and tanx=1, so here is the Qeustion, what is the smallest angle which satisfies the equation cosx-cosxcotx=0 in the interval ( 0,pi)

Answer 26

cosx(1-cotx) = 0. x = pi/2, pi/4

Answer 27

I factored out a cosx from both terms. cos(pi/2) = 0, which will result in 0. And 1-cotx is 0 when x = 45 degrees or pi/4 as discussed earlier.

Answer 28

Sorry, pi/2 is 90 degrees.

Answer 29

Oops, then that mean's the smallest angle that'll give you 0 is 45 degrees.

Answer 30

where did u get pi/2 and pi/4??

Answer 31

means*

Answer 32

From when I factored out the cosx from both terms: cosx(1-cotx) = 0. When does cosx = 0, when does (1-cotx) = 0. In the first case, x has to be 90 degrees b/c cos(90) is 0. In the second case, since we already said cot(45) is 1, (1-1) = 0, which will make the entire equation = 0.

Answer 33

so the answer would be 0 ??

Answer 34

No, the answer will be 45 degrees. That's the smallest angle that you can plug where you can get the answer of 0.