Lim x* sen(1/x) when x goes to 0. I did and obtain 1, but, in the book, the answer is 0!

Question

Lim x* sen(1/x) when x goes to 0.  I did and obtain 1, but, in the book, the answer is 0!

anonymous · Answer

Did you use a substitution?

anonymous · Answer

Just keep in mind, if you perform the following substitution

$$ u = \frac{1}{x} $$ you want to change the limit that is being approached, in order to get the correct answer. When x approaches infinity, u goes to zero.

Otherwise, use a Series representation.

jpsmarinho · Answer

Which is Series representation?

jpsmarinho · Answer

Do this is wrong?
  $$\lim_{x \to 0} \frac{sin(1/x)}{1/x}=1$$

anonymous · Answer

0 is the answer

anonymous · Answer

that is not the answer. :(
You can use the squeeze thm for this.

anonymous · Answer

@rainaby .....Don't just give answers man.

anonymous · Answer

no its simple see for any x sin(x) is finite and multiply it with 0 u get 0 as answer

anonymous · Answer

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