Final answer:
To find the limit of the given expression, divide the numerator and denominator by the highest power of t and simplify the expression.
Step-by-step explanation:
To find the limit of the given expression, we divide the numerator and denominator by the highest power of t. In this case, the highest power is t³. Therefore, we divide both terms by t³:
limt->[infinity] (3 * t³ + 5 * t² + 4) / (7 * t³ - 7 * t² - 8 * t + 4)
Dividing by t³, we get:
limt->[infinity] (3 + 5/t - 4/t³) / (7 - 7/t - 8/t² + 4/t³)
As t approaches infinity, the terms with 5/t and 4/t³ go to zero, and the expression simplifies to:
limt->[infinity] (3) / (7)
Therefore, the limit is 3/7.