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Miike012
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limits -- Prove that xsin1/x approaches 0 near 0
Prove that xsin1/x approaches 0 near 0.
Similiar Proof from book
|sin1/x| ≤ 1
| xsin1/x | ≤ |x| for all x not equal to 0, so we can make |xsin1/x|< ε by requiring that |x| < ε and not equal to 0.
MY QUESTION: Prove x2sin1/x approaches 0 near 0.
According to the book, if ε>0, to ensure that |x2sin1/x |< ε we need only require that |x| < ε and not equal to 0.
shouldnt |x| be less that √ε? Hence |x2 | < ε and |x|< √ε.
Prove that xsin1/x approaches 0 near 0.
Similiar Proof from book
|sin1/x| ≤ 1
| xsin1/x | ≤ |x| for all x not equal to 0, so we can make |xsin1/x|< ε by requiring that |x| < ε and not equal to 0.
MY QUESTION: Prove x2sin1/x approaches 0 near 0.
According to the book, if ε>0, to ensure that |x2sin1/x |< ε we need only require that |x| < ε and not equal to 0.
shouldnt |x| be less that √ε? Hence |x2 | < ε and |x|< √ε.