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The appearance of logarithm
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The Number `E' by Tanvi Jain
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- 1 The number ' e'
- 2 What is e? Is this just a number
- 3 The first hint of
- 4 How will you solve this? We will need to solve for the equation:
- 5 A question on compound interest
- 6 If the amount is compounded twice, each time at the interest rate of 50%.
- 7 Observations:
- 8 Let's see...
- 9 Logarithm and John Napier
- 10 So the problem of multiplication and division can be reduced to that of addition and subtraction.
- 11 Squaring a hyperbola
- 12 Coming to the early seventeenth century
- 13 Area of the region bounded by y = x", x = and x = a.
- 14 Similarly, the area of the region bounded by the curves y = x-",
- 15 A look at the hyperbola
- 16 The appearance of logarithm
- 17 The series for and the work of Newton
- 18 which implies ao = 0. Comparing the coefficient of y.
- 19 Derivative of an exponential function
- 20 Derivative of bx
- 21 The "natural "exponent Derivative of any exponential function is a constant multiple of the function itself.
- 22 The notation for the natural exponent
- 23 Is an integer?
- 24 rational or irrational
- 25 Since is not an integer, q 2 2. Hence q + 1 2 3.
- 26 Euler's proof of the irrationality of
- 27 The exponential function on complex numbers
- 28 Occurrences of
- 29 e'" Paradox
