Help on calculus please!

Question

Evaluate 

Answer 1

The limit has the indeterminate form 0/0

Multiply the numerator and denominator by √(x²+3) + 2 to obtain:

lim_x→₁[ (x²-1) /( (√(x²+3) + 2)(x - 1))

= lim_x→1 [(x+1) / (√(x²+3) + 2)= 2/4 = 1/2