Function End Behavior Worksheets Grade 12

1. lim(x→∞) (4x³ - 2x² + 5)/(3x³ + 7x - 1) = ?
2. Tane is a materials engineer developing a new type of ceramic coating for high-temperature applications. He models the thermal conductivity K (in W/m·K) of the coating as a function of temperature T (in Kelvin) using the function K(T) = (9T^3 - 7T^2 + 5T - 3) / (3T^3 + 2T - 1). As the temperature approaches extremely high values (T → ∞), what limiting thermal conductivity value does the coating approach?
3. A biomedical engineer is modeling the concentration of a new medication in a patient's bloodstream using the function C(t) = (3t^3 - 2t^2 + 5)/(t^3 - 4), where t represents hours after administration. As time approaches infinity, what value does the medication concentration approach, and what does this represent in terms of the drug's long-term behavior in the body?

…and 4 more problems

1. A right circular cone has a height of 12 cm and a base radius of 5 cm. A horizontal plane cuts through the cone parallel to its base, creating a smaller cone at the top and a frustum below. If the smaller cone has a volume exactly one-eighth the volume of the original cone, what is the height of the smaller cone?
2. lim(x→-∞) (9x⁵ - 7x³ + 5)/(3x⁵ + 2x² - 11) = ?
3. lim(x→-∞) (8x⁶ - 6x⁴ + 2)/(4x⁶ + 10x³ - 2) = ?

…and 4 more problems

1. lim(x→∞) (5x⁴ - 3x² + 7)/(2x⁴ + x³ - 8) = ?
2. lim(x→∞) (4x⁵ - 2x³ + 8)/(3x⁵ + 5x² - 1) = ?
3. Charlotte is a pharmaceutical researcher modeling the long-term concentration of a new antibiotic in a patient's bloodstream. The concentration C(t), measured in micrograms per milliliter (mcg/mL), is given by the function C(t) = (9t^3 - 14t^2 + 8) / (3t^3 + 7t - 12), where t represents time in hours after the initial dose. As time increases indefinitely (t → ∞), what concentration level does the antibiotic approach in the patient's bloodstream?

…and 5 more problems