18. If lim(xn) = x 0, show that there exists a natural number K such that if n ≥ K, then (1)/(

Name: 18. If lim(xn) = x > 0, show that there exists a natural number K such that if n ≥ K, then (1)/(2)x < xn < 2x.
Uploaded: 2021-07-19T15:43:15-08:00
Duration: 1 min 24 s
Channel: Julie Silva
Description: 18. If lim(xn) = x > 0, show that there exists a natural number K such that if n ≥ K, then (1)/(2)x < xn < 2x.

Question

18. If lim(xn) = x &gt; 0, show that there exists a natural number K such that if n ≥ K, then (1)/(

Julie Silva · Accepted Answer

Step 1: Given limx→x>0, we know that for any ε>0, there exists a δ>0 such that if 0

Question

18. If $\lim(x_n) = x > 0$, show that there exists a natural number K such that if $n \ge K$, then $\frac{1}{2}x < x_n < 2x$.

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