limit of frac functionI'm trying to find lim x → 0 ( ( e x − 1 ) ⋅ frac ⁡ ( 1 x ) )I thought maybe use squeeze theorem but then I have ( e x − 1 ) ⋅ ( ( 1 x ) − 1 ) ≤ ( e x − 1 ) ⋅ frac ⁡ ( 1 x ) ≤ ( e x − 1 ) ⋅ 1 x where frac ⁡ ( x ) = x − ⌊ x ⌋p.s - I can't use L'Hopipal rule.

Question

limit of frac functionI&#039;m trying to find      lim          x      →      0        (  (      e    x    −  1  )  ⋅  frac  ⁡      (          1      x        )    )I thought maybe use squeeze theorem but then I have  (      e    x    −  1  )  ⋅      (              (              1        x            )        −    1    )    ≤  (      e    x    −  1  )  ⋅  frac  ⁡      (          1      x        )    ≤  (      e    x    −  1  )  ⋅        1    x  where   frac  ⁡  (  x  )  =  x  −  ⌊  x  ⌋p.s - I can&#039;t use L&#039;Hopipal rule.

Denier5h · Accepted Answer

The fractional part is always between   0 and   1, and       e    x    −  1  →  0 as   x  →  0, so you have something between   0  ⋅  (      e    x    −  1  ) and   1  ⋅  (      e    x    −  1  ), and those both approach   0

Orion Cervantes · Accepted Answer

Hintwe have that  ∀  X  ∈      R        0  ≤  X  −  ⌊  X  ⌋  ≤  1    ⟹    ∀  x  ≠  0          |    f  (  x  )      |    ≤      |        e    x    −  1      |    .the limit when   x  →  0 is zero.

limit of frac function I'm trying to find \lim _(x->0) ((e^x-1)* ((1)/(x))) I thought maybe use squeeze theorem but then I have (e^x-1)(((1),(x))-1)<=(e^x-1)(1/x)\le (e^x-1)*1/x where frac(x)=x−⌊x⌋.p.s - I can't use L'Hopipal rule.

Answered question

Answer & Explanation

New Questions in Pre-Algebra