(sqrt5(a+h)-sqrt(5a))/h. find the limit as h approaches 0

Answer 1

Recall that f'(a) = lim_h→0 [ {f(a+h) - f(a)) / h ]

So, the given limit is f'(a) for the function f(x) = √(5x)

f'(x) = (1/2)(5x)^-1/2(5) = 5 / (2√(5x))

Therefore, f'(a) = 5 / (2√(5a))