1. To find the limit of the expression lim x->0 (√(2x+1) - 1) / x, we can use the limit properties and algebraic manipulation.

First, let's simplify the expression by rationalizing the numerator:
lim x->0 (√(2x+1) - 1) / x
= lim x->0 (√(2x+1) - 1) / x * (√(2x+1) + 1) / (√(2x+1) + 1)
= lim x->0 (2x + 1 - 1) / (x * (√(2x+1) + 1))
= lim x->0 2x / (x * (√(2x+1) + 1))
= lim x->0 2 / (√(2x+1) + 1)

Now, we can substitute x = 0 into the expression:
lim x->0 2 / (√(2x+1) + 1)
= 2 / (√(2(0)+1) + 1)
= 2 / (√1 + 1)
= 2 / (1 + 1)
= 2 / 2
= 1

Therefore, the limit of the expression lim x->0 (√(2x+1) - 1) / x is 1.

2. To find the limit of the expression lim x-> -∞ (x+1)(2x-3) / (x^2-4), we can use the limit properties and algebraic manipulation.

First, let's simplify the expression by factoring the numerator and denominator:
lim x-> -∞ (x+1)(2x-3) / (x^2-4)
= lim x-> -∞ (x+1)(2x-3) / ((x+2)(x-2))

Now, we can cancel out the common factor of (x+1) in the numerator and denominator:
lim x-> -∞ (2x-3) / (x-2)

Next, we can divide every term in the expression by x to simplify further:
lim x-> -∞ (2 - 3/x) / (1 - 2/x)

Now, we can take the limit as x approaches -∞:
lim x-> -∞ (2 - 3/x) / (1 - 2/x)
= (2 - 0) / (1 - 0)
= 2 / 1
= 2

Therefore, the limit of the expression lim x-> -∞ (x+1)(2x-3) / (x^2-4) is 2.