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

Answer 1

Christopher Agresta

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!

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Answer 2

Charles Anctil

To evaluate the limit (1/(x+2)-1/2)/x as x approaches 0, we can simplify the expression first. By finding a common denominator and combining the fractions, we get ((2- (x+2))/(2(x+2)))/x. Simplifying further, we have (2-x-2)/(2(x+2)x), which simplifies to -x/(2(x+2)x). Canceling out the x terms, we are left with -1/(2(x+2)). Finally, substituting x=0 into the expression, we get -1/4. Therefore, the limit of (1/(x+2)-1/2)/x as x approaches 0 is -1/4.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.