How do you evaluate the limit $(1/(x+2)-1/2)/x$ as x approaches $0$ ?

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Answer 1 · 2016-11-10T14:15:01

The limit is $-1/4$ .

$=lim_(x->0) ((2 - (x + 2))/(2(x + 2)))/x$

$=lim_(x->0) ((2 - x - 2)/(2(x+ 2)))/x$

$=lim_(x->0) ((-x)/(2(x+ 2)))/x$

$=lim_(x->0) (-x)/(2(x + 2)) xx 1/x$

$=lim_(x->0) -1/(2(x + 2))$

$= -1/(2(0 + 2))$

$=-1/4$

Hopefully this helps!

How do you evaluate the limit (1/(x+2)-1/2)/x(1/(x+2)-1/2)/x as x approaches 00?