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Algebra & Calculus

This guide explores the concept of limits in algebra and calculus, highlighting the conditions for continuity in functions. It answers questions related to investment returns with high interest rates and illustrates the importance of approaching the same value from both sides in limit calculations. We discuss continuous functions, present student activities, and investigate whether given functions are continuous at specific points. Ideal for students looking to deepen their comprehension of these foundational mathematical concepts.

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Algebra & Calculus

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  1. Algebra & Calculus Limits

  2. Is 2 euro the best possible return If I invest €1after 1 year with an interest rate of 100%?

  3. 2.7 2.71 2.718 2.7182 2.71828 2.718281 2.7182818 2.71828182 2.718281828 2.7182818284..............

  4. Assuming that the domains of the following functions are over R, write out the accurate domain for each function.

  5. The practical value we use is called a limit and exists if the function approaches the same value from the left and right.

  6. Concept of a limitStudent Activity Page 3

  7. Concept of a limitStudent Activity 6 6 No

  8. Understanding the Geometrical Meaning of ‘Limits of Functions’

  9. Understanding the Geometrical Meaning of ‘Limits of Functions’

  10. Understanding the Geometrical Meaning of ‘Limits of Functions’

  11. Continuous Functions

  12. For a function to be continuous at a point it must fulfil all these 3 conditions: Are the above graphs continuous functions at x = 2?

  13. Continuous – Yes / No

  14. Continuous – Yes / No

  15. Determine whether each of the following functions are continuous. • If not state where the function is discontinuous Page 4

  16. a) b) c) d) e) f) y = f(x) y = f(x) y = f(x) a a a a y = f(x) y = f(x) y = f(x) a a Page 5

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