# How do you prove that the limit # 3/sqrt(x-5) = ∞# as x approaches #5^+# using the formal definition of a limit?

Please see below.

Finding the proof This explanation of finding the proof is a bit long. If you just want to read the proof, scroll down.

By definition,

Writing the proof

Proof:

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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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