I need to save some plots in EPS and TIFF files with 900-1200 dpi. I am trying the usual Export function. With EPS, it always saves in very low resolution, no matter the ImageResolution I set (I think EPS is not compatible with ImageResolution, but I still need to save the file with specified dpi in EPS format and don't know how). With TIFF , for 900 dpi, Mathematica takes several seconds and then aborts and warns "No more memory available. Mathematica kernel has shut down. Try quitting other applications and then retry." With lower dpi, TIFF works, but produces gigantic files (e.g., 85 GB for 500 dpi), so the questions would be why is it producing so ridiculously huge files and how to avoid it. I have 3 GB in RAM.

The images I'm trying to save are more complicated, so it runs out of memory faster, but the next examples are much more easier to read and the behaviour is the same.

Examples with EPS (both of them produce a 94 kb file):

Export["Example1.eps", 
 Plot[{x^2, 1 - x, 3 x, (x - 1)^1.5, -x, E^x, Log[x]}, {x, -5, 5}], 
 ImageResolution -> 100]

Export["Example2.eps", 
 Plot[{x^2, 1 - x, 3 x, (x - 1)^1.5, -x, E^x, Log[x]}, {x, -5, 5}], 
 ImageResolution -> 1000]

Examples with TIFF (the first one produces a 45 MB file, the second one runs out of memory):

Export["Example3.tiff", 
 Plot[{x^2, 1 - x, 3 x, (x - 1)^1.5, -x, E^x, Log[x]}, {x, -5, 5}], 
 ImageResolution -> 1000]

Export["Example4.tiff", 
 Plot[{x^2, 1 - x, 3 x, (x - 1)^1.5, -x, E^x, Log[x]}, {x, -5, 5}], 
 ImageResolution -> 2000]

Thanks in advance