Worksheet: Limits in a Real-World Context

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

Q1:

A company produces greetings cards with an initial cost of 6,000 LE and an extra cost of 1 2 L E per card. The total cost is given by 𝐢 = 1 2 π‘₯ + 6 , 0 0 0 where π‘₯ is the number of produced cards. The maximum number of cards the company can produce a day is 15,000. Find the cost when the company produces an infinite number of cards.

  • A 6,000 LE
  • B0 LE
  • C 7,500 LE
  • D ∞
  • E 15,000 LE

Q2:

A company’s profit in LE as a function of its advertisement expenditure π‘₯ is 𝑓 ( π‘₯ ) = 0 . 2 π‘₯ + 3 4 π‘₯ + 1 2 3  . Determine the profit as π‘₯ approaches 100 LE.

Q3:

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

Q4:

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

  • A4
  • B10
  • C 2 √ 2 9
  • D 2 √ 2 1

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