## To compute the limit of the expression (sqrt(4+h) - 2) / h as h approaches 0, you can follow these steps:

Step 1: Multiply the numerator and denominator by the conjugate of the numerator, which is (sqrt(4+h) + 2). This is done to eliminate the square root in the numerator.

(sqrt(4+h) - 2) / h * (sqrt(4+h) + 2) / (sqrt(4+h) + 2)

Step 2: Simplify the numerator by using the difference of squares formula.

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

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

h / (h * (sqrt(4+h) + 2))

Step 3: Simplify the expression by canceling out the common factor of h in the numerator and denominator.

1 / (sqrt(4+h) + 2)

Step 4: Take the limit as h approaches 0.

lim(h->0) 1 / (sqrt(4+h) + 2)

Plugging in h = 0 into the expression gives:

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

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