# How do you evaluate the limit #(sqrt(4+h)-2)/h# as h approaches #0#?

you could use L'Hopital here too

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To evaluate the limit (sqrt(4+h)-2)/h as h approaches 0, we can use the concept of limits and algebraic manipulation. By applying the limit definition, we can simplify the expression:

(sqrt(4+h)-2)/h = [(sqrt(4+h)-2)/h] * [(sqrt(4+h)+2)/(sqrt(4+h)+2)] = (4+h-4)/(h * (sqrt(4+h)+2)) = h/(h * (sqrt(4+h)+2)) = 1/(sqrt(4+h)+2)

As h approaches 0, the expression simplifies to:

1/(sqrt(4+0)+2) = 1/(sqrt(4)+2) = 1/(2+2) = 1/4

Therefore, the limit of (sqrt(4+h)-2)/h as h approaches 0 is 1/4.

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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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