Respuesta :

LammettHash
I assume you're familiar with the limit

[tex]\displaystyle\lim_{x\to0}\frac{\sin ax}{ax}=1[/tex]

for [tex]a\neq0[/tex]. We write the given limit in this form:


[tex]\displaystyle\lim_{x\to0}\frac{\sin(-2x)}x=-2\cdot\lim_{x\to0}\frac{\sin(-2x)}{-2x}[/tex]

The limit on the RHS is 1, so we're left with -2.

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