# How do you determine the limit of #(x+5)/(x-2)# as x approaches 2+?

The limit tends to

And so on.

This is because the division of a number by an extremely small one gives us an extremely large answer.

Therefore, we can say:

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To determine the limit of (x+5)/(x-2) as x approaches 2+, we substitute the value 2 into the expression. However, since the denominator becomes zero at x=2, we cannot directly substitute the value. In this case, we can use the concept of one-sided limits.

To find the limit as x approaches 2+ (from the right side), we evaluate the expression for values of x that are slightly greater than 2. By substituting x=2.1, x=2.01, x=2.001, and so on, we observe that the expression approaches positive infinity. Therefore, the limit of (x+5)/(x-2) as x approaches 2+ is positive infinity.

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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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