What is the limit as x approaches infinity of 4xsin(1/x)?

Question

Can you also show me how you get the answer?
Thank you so much!!

Answer 1

lim (x --> inf) 4x * sin(1/x)

Let t = 1/x as x --> inf, t --> 0

lim (t --> 0) 4 (1/t) * sin(t)

lim (t --> 0) 4 * sin(t)/t

lim (t--> 0) 4 * lim (t --> 0) sin(t) / t

= 4 * 1

= 4

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