Luis C.

asked • 06/19/19

Limit of x*sin(1/x) as X approaches 0

After those steps, the result is wrong, and I can't understand what's wrong.

lim(x→0) x·sin(1/x) =

a = 1/x

lim(x→0) x·sin(a)·a/a=

lim(x→0) (x·sin(a)·a)/a=

since lim(x→0) sin(a)/a = 1, than:

lim(x→0) x·a=

lim(x→0) x·1/x=

lim(x→0) x/x = 1

But the right answer is 0, how can this be possible?

1 Expert Answer


Hadi B. answered • 06/20/19

BS in Mathematics with 5+ years of tutoring experience

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