Final answer:
The limit of 1/x as x tends to infinity is 0. This is because as x increases, the quotient 1/x becomes increasingly smaller, approaching zero. Option a) 0 is the correct answer.
Step-by-step explanation:
The question asks us to find the limit of 1/x as x tends to infinity. As x becomes larger and larger, the value of 1/x gets closer and closer to zero. This is because with each increase in the value of x, the division results in a smaller fraction, since we are dividing 1 by a larger number each time. In formal terms, for any positive value ε, we can find a value N such that for all x > N, |1/x| < ε, this fulfills the mathematical definition of a limit.
The correct option for the limit of 1/x as x tends to infinity is therefore option a) 0. This is an example of a horizontal asymptote where the graph of the function y = 1/x approaches the x-axis (y=0) as x goes to infinity.