Lim (as n -> inf) of (1-sin(n))/n.
What I thought of was splitting these up to lim 1/n - lim sin(n)/n. So the limit of 1/n -> 0 and the limit of -sin(n)/n is ..... 0?
If I understand correctly the limit of that sin(n)/n is 1 when n -> 0 and is 0 when n -> inf?
I get confused with taking the limits of the trig functions. Are there any good sources online that could help summarize that process so I can learn those well? Thank you for all your help!! I really appreciate it!!
What I thought of was splitting these up to lim 1/n - lim sin(n)/n. So the limit of 1/n -> 0 and the limit of -sin(n)/n is ..... 0?
If I understand correctly the limit of that sin(n)/n is 1 when n -> 0 and is 0 when n -> inf?
I get confused with taking the limits of the trig functions. Are there any good sources online that could help summarize that process so I can learn those well? Thank you for all your help!! I really appreciate it!!
-
lim (1 - sinn)/n = 0
n-> ∞
Solved by inspection.
sinn oscillates between -1 and 1.
Therefore, the numerator, 1 - sinn, oscillates between 0 and 2.
The denominator approaches ∞.
Therefore, the fraction approaches 0.
n-> ∞
Solved by inspection.
sinn oscillates between -1 and 1.
Therefore, the numerator, 1 - sinn, oscillates between 0 and 2.
The denominator approaches ∞.
Therefore, the fraction approaches 0.