datamlistic
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Friday 20 February 2026 07:14:09 GMT
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Ted Courant :
Define e as the exponential base whose slope at x=0 is 1. Everything follows from this, including log properties and the standard limit definition of e.
2026-02-20 17:26:53
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knudvaneeden :
To find the limit 1 when h goes to zero, one can also use power series of e^x. That is equal to the sum of (x^k)/(k!) for k=0 to k->infinity thus same for e^h and working out equals h^0/0! + h^1/1! + h^2/2! + ... = 1 + h + h^2/2 + ... Thus subtracting 1 leaves h + h^2/2 + ... Dividing that by h leaves 1 + h/2 + ... Letting h go to zero leaves that 1. QED.
2026-02-20 16:40:02
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