Limit Calculation Worksheets Grade 12

1. Aroha sketches the graph of the function f(x) = (x^3 - 64) / (x - 4). On the coordinate plane, the graph appears to be a smooth curve everywhere except at x = 4, where there is a hole. What is the y-coordinate of that hole?
2. lim_{x→7} (x² - 49)/(x - 7) = ?
3. lim_(x→∞) (4x³ - 7x + 2)/(2x³ + 5x² - 3) = ?

…and 4 more problems

1. A biomedical engineer is modeling the concentration of a new drug in a patient's bloodstream over time. The concentration function is given by C(t) = (t² - 4)/(t - 2) for t ≠ 2, where t is measured in hours. To understand the drug's behavior at the critical time t = 2 hours, the engineer needs to determine the limit of C(t) as t approaches 2. What is this limit value?
2. A biomedical engineer is modeling the concentration of a new drug in a patient's bloodstream over time. The concentration function is given by C(t) = (3t² - 12)/(t² - 4) milligrams per liter, where t is time in hours after administration. As time approaches 2 hours, the function appears undefined. Determine what the concentration approaches as t gets arbitrarily close to 2 hours from both sides.
3. Evaluate the limit: lim(x→∞) [√(4x² + 3x - 1) - 2x]

…and 4 more problems

1. lim_{x→4} (x² - 16)/(√x - 2) = ?
2. A geometric pattern is formed by inscribing squares within squares. The largest square has side length 8 units. Each subsequent square is formed by connecting the midpoints of the sides of the previous square. As this process continues infinitely, what is the limit of the sum of the areas of all the squares?
3. lim_(x→∞) (5x³ + 2x² - 7)/(3x³ - x + 4) = ?

…and 3 more problems