Question

help
who can i work it out
lim x→0 6 sin x/x

Answer 1

what you mean to work it out? Proof it to you? The limit you have written above is one of the "fundamental limes", you can proof them by using the squeeze theorem. LaTeX does not work on my end, but I will type it out anyway.
\[\large \lim_{x \to 0 } \frac{\sin x}{x} =1\]

Answer 2

If you want to prove that identity then consider the following inequality:
\[\sin x \leq x \leq \tan x \]
you can verify that for yourself by using the geometric approach of the unit circle. if you manipulate the above inequality, you will straight end up at the point where you can apply the sandwich/squeeze theorem to obtain the desired answer.

Answer 3

factor it

Answer 4

give the limit

Answer 5

Are you working with the inequality?

Answer 6

omplete the table. (Round your answers to five decimal places. Assume x is in terms of radian.)
lim x→0
6 sin x
x
x −0.1 −0.01 −0.001 0 0.001 0.01 0.1
f(x) ?

Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to five decimal places.)
lim x→0
6 sin x/x

Answer 7

i got the table

Answer 8

oh ok, you need to complete that table on yourself you understand that part?
They give you various \(x\) values, for instance \(x_1=-0,1, x_2=-0.01, x_3=-0.001\) you are supposed to put them into your equation, where \(f(x)\) is equal to:
\[\large f(x)=6 \frac{\sin (x)}{x} \]

Answer 9

yes i understand that part

Answer 10

plug the various \(x\) values into the equation above and see what the equation approaches. That will be your limit (in that context only, not as a proof)

Answer 11

i dont got it :(

Answer 12

well that's the entire exercise already, you plug in small \(x\) values, you understand, the notation \(x \to 0\) just means "as \(x\) gets very very very small". In mathematics, \(x\) becomes infinitesimal small. But for a real application of that, you can just plugin small values of \(x\) into your calculator and see what happens.
\(x= 0.1\) is a small value of \(x\). However \(x=0.0001\) is even a smaller value of \(x\)

Answer 13

You said that you understand the part about completing your table, if you complete your table, you're done, that is the whole exercise. See what values \(f(x)\) takes on as \(x\) takes on a small value like for instance \(x=-0.0001\). Complete the table and reason out for yourself what the limit is.

Answer 14

it will be 6 right

Answer 15

exactly :-)

Answer 16

thanks

Answer 17

you're welcome

Answer 18

:)