Final answer:
The limit of sin x as x approaches infinity does not exist because the sine function oscillates continuously and does not settle towards a specific value.
Step-by-step explanation:
b. False. The question of what the limit of sin x is as x approaches infinity is generally considered an indeterminate form. The sine function oscillates between -1 and 1 for all real numbers, so as x grows without bound, the function continues to oscillate and does not approach any particular finite value. Therefore, the limit of sin(x) as x approaches infinity does not exist in the conventional sense, since it lacks a unique limit at infinity.
The statement is false. The limit of <strong>sin(x)</strong> as x approaches infinity does not exist. Unlike some functions, such as <strong>1/x</strong>, which have asymptotes or limits at certain points, <strong>sin(x)</strong> oscillates between -1 and 1 as x gets larger and larger, without approaching a specific value. Therefore, the correct answer is b. False.