The first sentence is correct. The preposition 'with' implies interaction with something. In the first sentence, you are basically saying that you will use a computer to finish the task.
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kenny19991. I will finish the task with a computer
2. I will finish the task by a computer.I'm not sure what the standard explanation is.
kenny1999how about "We go to school by bus?"by is used with most methods of transportation.
CalifJim kenny1999how about "We go to school by bus?"by is used with most methods of transportation.to [go / travel] by [bus / train / plane / taxi]with ( a ) is used with most hand-held tools.to accomplish a task with a [knife / hammer / broom / pencil]by -ing is used with procedures.to accomplish something by [writing a letter / making a contribution / joining a club /