# How do you find #lim 1+1/x# as #x->0^+#?

We may split the limit up as follows, recalling the fact that

Then,

Our result is

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The limit of 1 + 1/x as x approaches 0 from the positive side (x->0+) is equal to 1.

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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.

- How do you find the limit of #x^2cos(pi / x)# as x approaches 0?
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- How do you find the limit #(sqrt(x^2+1)-1)/(sqrt(x+1)-1)# as #x->0#?
- How do you find the limit of # (acota)/(sina) # as a approaches 0?
- How do you find the limit of #tan^-1(1/x)# as #x->0^+#?

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