lim x infinity sin x / x
lim x infinity sin x / x
\In this video, we evaluate the limit:
lim (x → ∞) sin(x) / x
We know that sin(x) oscillates between -1 and 1 for all values of x. Using this information, we apply the Squeeze Theorem to show that as x approaches infinity, sin(x)/x approaches 0.
Step-by-step explanation:
1. We start by recognizing that sin(x) is bounded between -1 and 1.
2. We divide the inequality by x to get -1/x ≤ sin(x)/x ≤ 1/x.
3. As x gets larger, both -1/x and 1/x approach 0.
4. Using the Squeeze Theorem, we conclude that the limit of sin(x)/x as x approaches infinity is 0.
Watch the full explanation and see how the Squeeze Theorem helps us find this limit!
#Calculus #Limit #Mathematics #SqueezeTheorem #Infinity #sinx