limit as x approaches infinity. (sin2x)/(x)

answer is 0. show me how please. thanks in advance =)

1 answer

As x approaches infinity, the range of sin(2x) takes on the upper and lower limits of +1 and -1.
Since Lim 1/∞ and Lim -1/∞ both equal to zero as x→∞, we conclude by the "sandwich rule" or the "squeeze theorem" that the limit of sin(2x)/x lies between the two, namely 0.