Question

Why limit sin(7x)/(4x) as x->0 from the left is 7/4?

Answer 1

\[\lim_{x \rightarrow 0}\frac{ \sin 7x }{ 4x}\]

Answer 2

As \[x \rightarrow 0\] \[\sin (x) \approx x\]

Answer 3

Ezea, sorry, I did not get it.

Answer 4

You could plug in values to the function that are near 0 and see what happens. For instance x = .01, .001, .000001, .0000000001.

Answer 5

Or perhaps look at a picture of a right triangle and put an angle x inside and compare the value to the ratio sin(x).

Answer 6

Yes I saw on wolfram alpha, but algebrically? How does it work?

Answer 7

No L'Hôpital's Rule.