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 ?
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 ?
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.
Recall the formula [which is just the M.S. for tan(x)]:
tan(x)=x+\frac{1}{3}x^3+\frac{2}{15}x^5+\frac{17}{315}x^7+...
Substitute this in the limit and the two "x" will be cancelled.
Then devide the denominator and the numerator by x^3.
and the limit will be done by the direct substitution...