Recent content by Sweet_GirL

It depends on the function it self. Personally, I think integration by parts is the famous way of finding the reduction formulas.

You can use the comparison tests since sin(1/n) is positive since the angle (1/n) is in the first quadratic for n=1,2,3,... To test it, you could use the limit comparison test with a p-series, can you do that ?

I tried that but its not easy to find that f and also f must be positive

Still searching for a solution with standard tests ..

It must be solved by the standart test. Anyone ?

well, 1 - \sqrt[n]{n} \rightarrow 0 as n \rightarrow \infty and this will make no sense.

hello I have this one: \sum_{n=1}^{\infty} \left( 1 - \sqrt[n]{n} \right) mmmmm am sure it will be tested by using one of the comparison tests but am not getting it any help? this is not my homework, actually I finished my college 2 years ago.

Inverse function (Edited) Homework Statement Find the inverse function of : f(x)=e^x-e^{-x}+2 where x \geq 0 Homework Equations All what I did is : y=e^x-e^{-x}+e The Attempt at a Solution How in Earth can I solve this for x ?

This is the Ratio Test not the Limit Comparison Test. Also, you should write a_k not a_n.

as x becomes large, the two function tend to 1. And clearly they are increasing functions. so what do you suggest?

40-30 \neq 15 :redface: I think you mean 45-30 :smile:

m/s?? :smile:

Yes. There is a big difference in solving multivariable limits between the 2-path rule (which is y=mx .. etc) and the polar coordinates method. 2-path rule proves only that the limit D.N.E and does not prove the existence of the limit. Polar coordinates method proves both cases.

So the limit = ? The polar coordinates works also :)

Clearly, k=0 is a solution. to find the another solution you need to use an advanced topic: http://mathworld.wolfram.com/LambertW-Function.html