Using the properties of limits, find

Question

      x^(2) + 3x + 5
lim  ------------------
x->2  x^(3) - 4x + 1

Answer 1

lim    [(x² + 3x + 5)/(x³ - 4x + 1)]

x→2

Apply the limits.

Substitute 2 for x.

= [ (2² + 3*2 + 5)/(2³ - 4*2 + 1) ]

= (4 + 6 + 5)/(8 - 8 + 1)

= 15/1

= 15.