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

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To evaluate the limit (2-x)/(2/x-1) as x approaches 2, we substitute the value of x into the expression. However, this would result in division by zero. To overcome this, we simplify the expression by multiplying both the numerator and denominator by x. This gives us (2x - x^2)/(2 - x). Now, we can substitute x = 2 into the simplified expression, which gives us (2(2) - 2^2)/(2 - 2). Simplifying further, we get (4 - 4)/(0), which equals 0/0. This is an indeterminate form. To evaluate the limit further, we can factor the numerator as (2 - x)(2 + x) and cancel out the common factor of (2 - x) in the numerator and denominator. This leaves us with (2 + x)/(1). Substituting x = 2 into this expression, we get (2 + 2)/(1), which equals 4/1 or simply 4. Therefore, the limit of (2-x)/(2/x-1) as x approaches 2 is 4.

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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.

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.

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.

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