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Comprehensive Guide to Exponential and Logarithmic Functions: Geometric and Algebraic Approaches

Explore a detailed explanation of exponentials and logarithms using geometric and algebraic methods. Learn how to differentiate and integrate functions, understand natural logarithms, and work through exercises for practical application.

bruce-mendoza
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Comprehensive Guide to Exponential and Logarithmic Functions: Geometric and Algebraic Approaches

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  1. Differentiating exponentials and logarithms

  2. A geometric approach to f(x)=ex

  3. A geometric approach to f(x)=ex

  4. A geometric approach to f(x)=ex

  5. Do Q1, Q2, Q3, Q4, p.54 An algebraic approach to f(x)=ex

  6. A definition for f(x)=ex

  7. Calculating e

  8. Integrating ex Do Q5-Q11, p.54

  9. The natural logarithm

  10. Derivative of the natural logarithm The proof is a consequence of the ‘mini-theorem’ outlined on p.55. Do Exercise 4B, p.57

  11. The reciprocal integral This plugs a gap!!! Do Exercise 4C, pp.58-59

  12. Extending the reciprocal integral Do Q1, p.62 Do Misc. Exercise 4, Q1-Q18, pp.62-64

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