This is going to depend very much on where you live, as prices vary tremendously. If it’s a small town, though, ask around; it’s entirely possible that somebody local has a side business cutting trees in the winter time even if you don’t have a full-time local tree company. Depending on your town, check with garden centers, landscape services, or the feed store.
For ballparks, though, I just had a whole 45’ maple tree taken out and hauled away for $900, by a couple of good ol’ boys with a bucket truck (yes, I made sure they had liability insurance). A professional arborist had quoted $1500 to drop it; hauling would have been extra.
Heated with wood for about 10 years. I’ve cut down many a tree. Never a mishap.
But, you have to be dam careful. Recently, I had a dead pine tree that was leaning in a very bad direction. Right toward my shed. it was about 2 feet in diameter at its base. It would have to be roped up to take it down in the right direction.
But…
I had a guy on our property doing excavation work with a track hoe excavator. We looked it over, and ended up pushing the tree over by putting his bucket high on the tree and pushing. Worked pretty well. At least it missed my shed.
For a limb 40 feet in the air though, you need the pros that are good with rope work.
IME, you’ll pay much more for someone with a bucket truck then you will for guys who climb/use ladders. The crew that we use (ladders, ropes, climbing rig) has done a $500 job for us that a bucket truck quoted at $1700.
I handle most of our tree work. The ones that are too difficult for me, we try to let add up until we have a full day’s work for the tree service we use. The cost per tree is way lower if they spend the whole day, versus coming out to do an hour or two work.
Taking down one limb, you will pay for them driving there, setting up, taking the limb, and then driving to their next job. They likely have a minimum fee, probably around $200.
Bucket truck has a higher equipment cost, but rope and ladders has higher labor/risk cost.
Some areas, equipement is worth more than labor and limb, and some, labor and limb are worth more than equipement. Varies based on the individual as well.
To the OP, yeah, get a professional to do it, shop around and get a good price, but probably best not to go with the lowest price. Or at least, get someone else to do it and make sure to video.
Many of the classic run in the direction the tree is falling errors, as opposed to running perpendicular to it. Not saying I’d have the presence of mind to do it the right way myself, of course.
I remember it as a revelation during a kids safety presentation when the speaker told the kids to not try and run down the street to get away from the stranger in a van - instead run in away from the road. It was obvious when he said it, but I had never considered it before (and of course, movies always show a person running down a street being chased by a car).