One sided limit question

**Vamz** · November 6th 2010, 01:42 PM

$ \frac{12sin^3x}{12x^3} $
$ \lim x \to 0^- $

Heres what I have...
can be rewritten as:
$ \frac{12(sinx)^3}{12x^3}=\frac{(sinx)^3}{x^3}=\fra c{sinx}{x}*\frac{sinx}{x}*\frac{sinx}{x}=1*1*1=1 $

Up to this point, am I correct? How does the fact that it wants the limit as x approaches zero from the left? I only know how to work with these one-sided limits in a peicewise function. What do I do from here & what do I need to learn to solve one sided limits that are NOT in a peicewise function?

Thanks!

**mr fantastic** · November 6th 2010, 02:13 PM

Originally Posted by Vamz

$ \frac{12sin^3x}{12x^3} $
$ \lim x \to 0^- $

Heres what I have...
can be rewritten as:
$ \frac{12(sinx)^3}{12x^3}=\frac{(sinx)^3}{x^3}=\fra c{sinx}{x}*\frac{sinx}{x}*\frac{sinx}{x}=1*1*1=1 $

Up to this point, am I correct? How does the fact that it wants the limit as x approaches zero from the left? I only know how to work with these one-sided limits in a peicewise function. What do I do from here & what do I need to learn to solve one sided limits that are NOT in a peicewise function?

Thanks!

$\displaystyle \lim_{x \to 0^-} \frac{12 \sin^3 (x)}{12 x^3} = \lim_{x \to 0^+} \frac{12 \sin^3 (x)}{12 x^3} = \lim_{x \to 0} \frac{12 \sin^3 (x)}{12 x^3} = 1$ .

**Archie Meade** · November 6th 2010, 02:19 PM

Originally Posted by Vamz

$ \frac{12sin^3x}{12x^3} $

$ \lim x \to 0^- $

Heres what I have...
can be rewritten as:

$ \frac{12(sinx)^3}{12x^3}=\frac{(sinx)^3}{x^3}=\fra c{sinx}{x}*\frac{sinx}{x}*\frac{sinx}{x}=1*1*1=1 $

Up to this point, am I correct? How does the fact that it wants the limit as x approaches zero from the left? I only know how to work with these one-sided limits in a peicewise function. What do I do from here & what do I need to learn to solve one sided limits that are NOT in a piecewise function?

Thanks!

$x=-u$

$x\rightarrow\ 0^-\Rightarrow\ u\rightarrow\ 0^+$

$Sinx=Sin(-u)=-Sinu$

$\displaystyle\frac{Sinx}{x}=\frac{-Sinu}{-u}=\frac{Sinu}{u}$

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