lim x>1 (lnx/sinpix)

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.

lim x>1 (lnx/sinpix)

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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

Since since sinpi is 0 (sinpi/x = 0 b/c x goes to 1), we have an indeterminate form (0/0). We can use L'Hopital's rule: take the derivative of the top and bottom. Get... (1/x)/cos(pi/x)(-pi/x^2) Plug in x=1 and get 1/(-1)(-pi) = 1/pi The answer is 1/pi
Another method is by series. Realizing lim x>1 (lnx/sinpix) is the same thing as lim x>0 [ ln(1-x) / sin(pi(1-x)) ], and that sin(pi(1-x)) = sin(pi(x)) we get the new limit: lim x>0 [ ln(1-x) / sin(pi*x) ] we may then use taylor expansions of both functions: ln(1-x) = x + (1/2)x^2 + (1/3)x^3 + ... sin(pi*x) = pi*x - (1/3!)(pi*x)^3 + (1/5!)(pi*x)^5 - ... when placed in fractional form we may divide out an x, leaving 1 and a series on top, pi and some series on the bottom, as x -> 0 the series left on top and bottom obviously approach 0, leaving 1 and pi, the solution being 1/pi

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Not the answer you are looking for?

Search for more explanations.

Ask your own question