Evaluate the limit lim _{h → 0} √(4 + h) - 2 / h

Solution:

Lim_h→0 √(4 + h) - 2 /h

This is the concepts of limits

= lim_h→0 1/h (2(1 + h/4)^1/2 - 2)

Let the coefficient of higher order be m

= lim_h→0 1/h (2(1 + (1/2)h/4 + m(h²)) - 2)

= lim_h→0 1/h(2 + h/4 + m(h²) - 2)

= lim_h→0 1/h(h/4 + m(h²))

= lim_h→0 1/4 + m(h)

= 1/4

Evaluate the limit lim _{h → 0} √(4 + h) - 2 / h

Summary:

The limit lim h → 0 √(4 + h) - 2 / h = 1/4.