# What is the limit of #(3+h)^-1 -3^(-1/h)# as h approaches 0?

so the limit DNE

the limit of the sum is the sum of the limits

the sign of the exponent will be different coming at this from either side

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The limit of (3+h)^-1 -3^(-1/h) as h approaches 0 is -1/9.

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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 #(x+5)(1/(2x)+1/(x+2))# as #x->0^+#?
- How do you determine the limit of #(x^2-2x)/(x^2-4x+4)# as x approaches 2-?
- How do you find the limit of #(x^2+x-6)/(x^2-9)# as #x->-3#?
- How do you find the limit of #(1/x-1/2)/(x-2)# as #x->2#?
- How do you find the limit #ln(x^2+1)/x# as #x->0#?

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