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I think it must be 1 converge

because the term that I circled it equal to zero !

I'm I right ?

xvxvxv Mar 17, 2015

#1**+5 **

Here is the graph.

https://www.desmos.com/calculator/orgvwef1o3

Why does what you circled =0 ??

What does diverge and converge mean?

Thinking about what they 'may' mean this doesn't really do either does it?

I know I am out of my depth here.

I guess I am hoping someone will teach me something that is easy to learn. (Well one can dream) :)

Melody Mar 18, 2015

#2**+10 **

Like Melody, I'm on shaky ground here....so.....you might have to take this with a grain of salt....

By the Integral Test, the function in the integrand must be eventually positive * and* decreasing on the interval of interest - in this case, 0 to ∞.

Here's the graph of y = cos(x)*e^(-sin(x))

.....https://www.desmos.com/calculator/ho13rj5sjr

Note that this function is * not* eventually positive and decreasing on the interval (it is periodic).....thus.....the integral diverges

That's my two cents worth.....

Alan??? heureka???....to the rescue???

CPhill Mar 18, 2015