Worksheet: Limits in a Real-World Context

In this worksheet, we will practice applying limits in real-life applications.

Q1:

A company’s profit in LE as a function of its advertisement expenditure π‘₯ is 𝑓(π‘₯)=0.2π‘₯+34π‘₯+123. Determine the profit as π‘₯ approaches 100 LE.

Q2:

In the figure below, points 𝐴 and 𝐡 lie on a circle of center 𝑀 and radius 1. Point 𝐢 is chosen so that π‘€πΆβŸ‚π΄π΅. Setting π‘₯ to the length of 𝑀𝐢 and 𝑦 to the length of 𝐴𝐡, what is the limit of 𝑦 as π‘₯β†’0?

Q3:

Using the figure below, determine the limit of length 𝑦 as the measure of πœƒ tends to πœ‹2.

  • A4
  • B10
  • C2√21
  • D2√29

Q4:

A car moves with velocity 𝑣(𝑑)=500π‘‘βˆ’1,000π‘‘βˆ’4/kmh. Find the velocity of the particle as 𝑑 approaches 2 hours.

  • A100 km/h
  • B250 km/h
  • C125 km/h
  • D0 km/h
  • E1 km/h

Q5:

A train moves with acceleration π‘Ž(𝑑)=2𝑑𝑑/sinms. Find the acceleration of the train as 𝑑 approaches 0 seconds.

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