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Question
Why when the exponet is 0 the answer is 1
Hi Aaron,
exp(0)=1 is true by definition.
If we let y=exp(x), it has an inverse function (natural logarithm) given by ln(y)=x. Having exp(0)=1 ensures that both curves are continuous and differentiable (in essence, being very smooth) in the limit as x goes to 0, whether we approach the point from the positive or negative end of the axis.
This is consistent with a well known result which states that "in the limit as x goes to infinity, any number "a" raised to the power of 1/x converges to 1".
viz., lim x->infinity a^(1/x) = 1
Numerical example: you can think of this as taking 10^(0.0000000001), this approaches 1.
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Josh
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When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.
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