Limits Concept Worksheets Grade 12

1. From graph: as x→7, f(x)→?
2. A particle moves along a curve with its position function given by f(x) = (x^3 - 8)/(x^2 - 4) for x ≠ 2. Determine the limit of f(x) as x approaches 2, which represents the instantaneous position the particle would approach at that moment.
3. lim(x→∞) (3x² + 2x - 1)/(2x² - x + 5) = ?

…and 5 more problems

1. A solid is formed by rotating the region bounded by the curve y = sqrt(x), the x-axis, and the vertical line x = 4 about the x-axis. Using the disk method, describe the volume of this solid as a definite integral. What is the integral expression for the volume?
2. Emma is analyzing the rate at which a chemical reaction produces product. The amount of product P(t) in grams after t minutes is modeled by the function P(t) = (t^2 - 16)/(t - 4). She needs to determine what amount of product the reaction approaches as time gets very close to 4 minutes, even though the function is undefined at exactly t = 4 minutes.
3. A pharmaceutical company is modeling the concentration of a new drug in a patient's bloodstream using the function C(t) = (3t² - 12)/(t - 2), where t is time in hours after administration. The researchers need to determine what concentration the drug approaches as time gets very close to 2 hours, when the function appears undefined. What is this limiting concentration value?

…and 4 more problems

1. Noah is analyzing the behavior of a function f(x) defined as follows: f(x) = (x^3 - 27)/(x - 3) for x ≠ 3. He creates a table of values for x approaching 3 from both sides. Using the table below, what is the limit of f(x) as x approaches 3? x | 2.9 | 2.99 | 2.999 | 3.001 | 3.01 | 3.1 f(x) | 25.21 | 26.8201 | 26.982001 | 27.018001 | 27.1801 | 28.81
2. Matiu is studying the velocity of a drone as it approaches a landing pad. The drone's height above the ground (in meters) at time t seconds is given by the function h(t) = (t^3 - 27) / (t - 3), which is undefined at t = 3 seconds. To program a smooth landing, Matiu needs to know the height the drone approaches as t gets very close to 3 seconds from either side. What value does the height approach?
3. Olivia is studying the behavior of a function f(x) defined by the following table. As x approaches 3 from both sides, what is the limit of f(x)? x f(x) 2.5 1.75 2.9 1.95 2.99 1.99 2.999 1.999 3.001 2.001 3.01 2.01 3.1 2.1 3.5 2.5

…and 4 more problems