Hello and welcome to the forum.
While it would be of help to see the rug as a whole, the rug you provided photographs to above does in fact appear to be a machine made carpet.
There are five main indicators I am using to understand this.
1. From what I see, there is also a post factory production binding tape applied on one end (as seen in the last attachment), which is also indicative of a machine made rug (or more often, a runner). You rarely ever see this applied to an Oriental Rug.
2. The pattern ends abruptly. This is not unusual to find in a machine made rug, as often runners are cut from a very long roll which may come from a factory in excess of 100', and then is finally cut down to a custom size for stair application. Mitering, or "finishing the ends" with a border is usually later implemented to make the rug appear more complete. This is done by using excess material, or linear footage of the rug as pieces that may later be patched to the ends of the rug to make the rug more presentable.
3. The orientation of the knots, and the precise fashion of creation also alludes to a machined construction.
4. The surging on the side of the rug (not the red tape, but the part affixed to the edge with the border), also alludes to machined edging.
5. The last indicator is a little tough to tell by the pictures as I cannot see the full scope of the rug. However, from experience, I can make an educated guess that the cut side with red binding tape is probably the width of the rug. Due to the nature of production (in the majority of machine made carpets), they typically are woven in a landscape format rather than a portrait format. This is a little difficult to explain, but what I am getting at here is it appears as though the technique of manufacturing also implies the rug is machine made, as the orientation of knots is opposite that of a hand knotted rug.
Overall I am pretty certain that this is a machine made carpet: especially considering any one of the above mentioned elements, not to mention all characteristics combined.
Monetarily (or in consideration of resale), I would say the rug at hand does not have a particularly high value, and an appraisal would not be necessary. However, if you would like further information, simply post a picture of the full rug (with description of condition - low pile, worn areas, stain, etc.), as well as the exact size, and I can probably give you an approximate value.
In terms of testing the fibers for wool or synthetic (be careful when you do this - if you don't feel comfortable ask for someone to help), you may
attempt to pull a knot out from the reverse side of the carpet. If this is too difficult to do, as sometimes it may be, you may clip a single small sample from the pile of the rug in an inconspicuous area. Be sure that you take as little as possible, and from an area that has an abundance of that particular color (so as to not interfere with the design of the rug.)
Bring the fiber to an open area with a cup of water nearby. Hold it with some old metal tweezers you don't particularly care about, and burn the sample piece with a match or lighter. If the odor of the sample smells like burned hair, you either have silk or wool. If the odor smells otherwise, it's probably a synthetic carpet. If you need a good indicator of what burned hair smells like, pull a strand from your friend, dog, cat, significant other, and try testing that to compare.
For more information on how to tell if a rug is machine made or hand knotted,
take a look at this post. If you have IE 6.0, you'll have to scroll way down before you see the content show. Pay particular attention to the edgine on machine made rugs shown towards the bottom.