Evaluate the limit for .

First we write and . Then we use the expansion of (p. 287), to obtain expansions for and ,

Therefore, we have

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Stumbling Robot

A Fraction of a Dot
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Find the limit as *x* goes to 0 of * (a*^{x} – 1) / (b^{x} – 1)

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Evaluate the limit for .

First we write and . Then we use the expansion of (p. 287), to obtain expansions for and ,

Therefore, we have

For those asking, o(x) is little o notation and it means different things in different cases but here it means *some* function f(x) such the quotient f(x)/x approaches 0 as x approaches 0. The definition in Apostol’s book was stated briefly and then Apostol started abusing the notation without explaining everything.

Wt is 0 (x) can anyone ans

that is e(x)

what is o(x)