Evaluate the following limits:
Since the form is indeterminant
Method 1: factorization
Since a3 + b3 = (a + b)(a2 + b2-ab) & a2-b2 = (a + b)(a-b)
Since a3 + b3 = (a + b)(a2 + b2-ab) & a2-b2 = (a + b)(a-b)
= (√4 + 2)(4 + 4)
= (2 + 2)(4 + 4)
= 32
Method 2: By L hospital rule:
Differentiating numerator and denominator separately:
= 4(4)3/2
= 32