Question

lim x → ∞ (12x^8-3)/3x^8-2x^7

Answer 1

Divide through all terms by the highest power of $x$:

$\dfrac{12x^8-3}{3x^8-2x^7}=\dfrac{12-\frac3{x^8}}{3-\frac2x}$

As $x\to\infty$, the terms with $x$ in the denominator will vanish, leaving us with

$\displaystyle\lim_{x\to\infty}\frac{12x^8-3}{3x^8-2x^7}=\frac{12}3=4$