How to find the limit of sin(x)/x as x approaches zero? For example, the problem is sin (2x)/ 8x, how to find the limit as x approaches to zero?

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

How to find the limit of sin(x)/x as x approaches zero? For example, the problem is sin (2x)/ 8x, how to find the limit as x approaches to zero?

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

will it be 1/4 since the limit of sin(x)/x is equal to 1?
We know that \[\lim_{x \rightarrow 0} \frac{\sin x}{x} = 1\] Looking at the given problem \[\lim_{x \rightarrow 0} \frac{\sin 2x}{8x} \] In order to get the problem to look like the form sin x / x, we need the denominator of the fraction to equal 2x. Setting the bottom to 2x, the limit looks like this: \[n \ \lim_{x \rightarrow 0} \frac{\sin 2x}{2x} \] In order for the above to be true, we would have to multiply the limit by some number \(n\). That's what you have to find.
Yeah, it works out to be 1/4.

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

ah okay thanks! one more question, why is it that \(\lim_{x \rightarrow 0} \frac{\sin x}{x} = 1\) ? Is there a proof that it is equal to 1?
I just know about it but I never learned the reason behind it

Not the answer you are looking for?

Search for more explanations.

Ask your own question