Question

Pointwise Limits of Functions Find the limit f ₙ →f. 1. fₙ (x)=nsin(x) / 5n+1

​

Answer 1

The limit fₙ→f for the given function fₙ(x) = (nsin(x)) / (5n+1) is 0 for all values of x.

Step-by-step explanation:

To find the limit fₙ→f for the function fₙ(x) = (nsin(x)) / (5n+1), we can use the concept of pointwise limits. The limit of fₙ(x) as n approaches infinity is the value that f(x) approaches as n gets larger and larger. In this case, as n approaches infinity, the numerator nsin(x) grows indefinitely while the denominator 5n+1 also grows indefinitely. Therefore, the limit of fₙ(x) is 0 for all values of x. This means that as n gets larger and larger, the function fₙ(x) gets closer and closer to the constant function f(x) = 0.