What is the limit of #sqrt(2-T) - (sqrt 2)/T# as T approaches 0?

Answer 1

I think the lateral limits are different:

As #T->0# we get that #sqrt(2-x)->sqrt(2)# but the term #-sqrt(2)/x#, depending upon the side you are approaching zero, should tend to #-oo# from the right and #+oo# from the left.

Graphically: graph{sqrt(2-x)-sqrt(2)/x [-10, 10, -5, 5]}

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Answer 2

The limit of sqrt(2-T) - (sqrt 2)/T as T approaches 0 is -∞.

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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.

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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