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How do you find the limit of #(1)/(x-2)# x as it approaches 2 from the right?

Answer 1

Emilia Aguilar

#+oo#

Let #epsilon in R^+, epsilon->0#

#lim_(x->2+epsilon) 1/(x-2) = lim_(epsilon->0) 1/(2+epsilon-2) = lim_(epsilon->0)1/epsilon=+oo#

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Answer 2

Ezekiel Alexander

To find the limit of (1)/(x-2) as x approaches 2 from the right, we substitute the value 2 into the expression. This results in 1/(2-2), which simplifies to 1/0. Since division by zero is undefined, the limit does not exist.

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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.