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How do you find the limit of #(1/x-1/2)/(x-2)# as #x->2#?

Answer 1

William Abdalla

#lim_(x->2)(1/x-1/2)/(x-2)#

Simplify the equation:

#= lim_(x->2)((2-x)/(2x))/(x-2)#

#=lim_(x->2)(2-x)/((2x)(x-2))#

Manipulate the equation to simplify further:

#=lim_(x->2)(-(x-2))/((2x)(x-2))#

Cancel and solve:

#=lim_(x->2)(-1)/((2x))=-1/4#

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Answer 2

Paisley Johnson

To find the limit of the expression (1/x - 1/2)/(x - 2) as x approaches 2, we can simplify the expression first.

First, we find a common denominator for the fractions in the numerator: 1/x - 1/2 = (2 - x)/(2x)

Now, we can rewrite the expression as: (2 - x)/(2x) / (x - 2)

Next, we can simplify further by multiplying the numerator and denominator by the reciprocal of the denominator: (2 - x)/(2x) * 1/(x - 2)

Now, we can cancel out the common factors: (2 - x)/(2x) * 1/(x - 2) = -(x - 2)/(2x(x - 2))

Finally, we can simplify the expression to: -(1/2x)

To find the limit as x approaches 2, we substitute the value of x into the simplified expression: -(1/2(2)) = -1/4

Therefore, the limit of (1/x - 1/2)/(x - 2) as x approaches 2 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.

How do you find the limit of #(1/x-1/2)/(x-2)# as #x-&gt;2#?

How do you find the limit of #(1/x-1/2)/(x-2)# as #x->2#?