Q1. 0
Q2. ⅔
Horizontal asymptotes are the limits of f(x) as x→∞ or -∞. This means, first, to replace all constants by zero in the denominator and numerator. In Q1, we get 2x/3x⁴ which reduces to 2/3x³. As x gets larger, this expression gets closer to zero (from the positive or negative side), so the asymptote is y=f(x)=0.
In Q2, the expression becomes 2x⁸/(3x⁸-2x⁷) which reduces to 2/(3-2/x). 2/x approaches zero as x gets larger, so the value of the expression approaches 2/3.