Evaluate the Limit

Question

evaluate lim x→2 √4x+1- 3/x-2

Answer 1

lim_x→2 [ (√(4x+1) - 3) / (x - 2)]

Direct substitution yields the indeterminate form 0/0'

Multiply and divide by √(4x+1) + 3 to get :

lim_x→2 [ 4(x-2) / ((x-2)(√(4x+1) + 3))] = lim_x→2 [4 / (√(4x+1) + 3)] = 2/3