Question

1. Using (€,gamma) definition show that lim x-0 (xsin 1/X) =0​

Answer 1

Answer:

Let ϵ>0 be given. Notice that

∣∣xsin1x∣∣≤|x|⋅1.

Then the desired inequality holds if |x|<ϵ=:.

Step-by-step explanation:

Let ϵ>0 be given. Notice that

∣∣xsin1x∣∣≤|x|⋅1.

Then the desired inequality holds if |x|<ϵ=:δ.