Science & Mathematics - 1 February 2007

I want to confirm if it's true that each time we get a limit equals to infinity, it means that our limit doesnt exist?
Also, assuming x approaches 0
I'm given the
lim [(3 cos 3x+a+2bx)/2x] = 4 ........(1)
It is known that the limit of 2x when x approaches 0 is 0.
And thus the
lim (3 cos 3x+a+2bx) = 0 ..............(2)
Can anyone explains to me how to get from (1) to (2) please?
p/s: Question asked to find values of a and b.
Thank you!

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