What's the limit?

lim(x→∞) -x / √(7x² + 4)

= lim(x→∞) [(-x)/x] / {[√(7x² + 4)]/x} ...... provided that x ≠ 0

= lim(x→∞) (-1) / √[(7x² + 4)/x²]

= lim(x→∞) (-1) / √[(7x²/x²) + (4/x²)]

= lim(x→∞) (-1) / √[7 + (4/x²)]

= (-1) / √[7 + lim(x→∞)4/x²)]

= (-1) / √[7 + 0]

= -1/√7

First of all, when you deal with a fraction, the best course of action is to try to determine whether the numerator or denominator has the highest degree. After simplifying the x^2 term in the radicand and bringing it outside the radical, it ends up having its exponent divided by 2, resulting in it just being x. At that point, you can get rid of the two x's, resulting in a fraction: -1/sqrt(7+4/x^2)

Since x is approaching infinity, having a variable in the denominator and a constant in the numerator will always result in that number becoming 0. So that means you are just left with -1/sqrt(7).

Later, you will learn about L'Hospital's rule, which makes solving for limit functions a lot easier in most cases.