Answer:
When x ⇒ +∞ and x ⇒ -∞, f(x) ⇒ 0 from the positive region.
Explanation:
Hi there!
Let´s write the function:
f(x) = (7x³ + 2) / (4x⁵ - 3x + 1)
When x ⇒ +∞ we can neglect the constant values (2 and 1). So:
f(x) ⇒ 7x³ /(4x⁵ - 3x)
f(x) ⇒ 7x³ / x(4x⁴ - 3)
f(x) ⇒ 7x² / 4x⁴
f(x) ⇒ 7/4x² ⇒ 0 from the positive region
when x ⇒ -∞
f(x) ⇒ 7/ 4x² ⇒ 0 from the positive region because x² is always positive.
Then when x is a very big number (positive or negative), f(x) will be approximately 0 and positive.