Prove that fn(x) = x/n rightarrow 0 show that it is uniform on any closed, bound

Question

Prove that fn(x) = x/n rightarrow 0 show that it is uniform on any closed, bounded interval[a,b].

Explanation / Answer

let the function f(x) has the domain D, then f(x) is said to be uniformly continuous on D iff for each ? > 0 there is z > 0.such that |f(x)- f(a)| < ? for x,a with in domain D and |x - a| 0 for which no z can be found which satisfies the above condition.Actually,none of the numbers x/n for n (where n is natural no) will suffice for z. This indicate that, for each n, there are numbers Xn,an (integers) such that |xn- an| = ? Which means that the sequences f(xn ) and f(an ) cannot converge to the same number Hence we can conclude that f(x) is uniformly continuous in the domain (a,b)

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