Tag Archives: limits

Calculus without limits 5: log and exp

The derivative of the log function can be investigated informally, as log(x) is seen as the inverse of the exponential function, written here as exp(x). The exponential function appears naturally from numbers raised to varying powers, but formal definitions of the exponential function are difficult to achieve. For example, what exactly is the meaning of exp(pi) or exp(root(2)).
So we look at the log function:-
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Calculus without limits 4: trignometric functions, cosine and sine

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It would be slightly more satisfying to set theta = f(t), where t is the time variable, but since dtheta/dt cancels out it doesn’t matter.

besides, this would require the dy/dx form of the derivative, and this seems to have gone out of fashion – poor Leibniz

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Limits

George, to his teacher:

I have now integrated my preconceived ideas and the enlightenments engendered by yourself, but I still have trouble differentiating between “the limit of” and “the limits of”.

George’s teacher, aside:

I think George would be better off writing a novel. he could call it “The Limits of Continuity”.

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