Why is this true?

Question

0

727

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How does this

Lim h-->0 (b^h-1 / h) = 1

Translate to this

Lim h-->0 (b^h) = Lim h-->0 (1+h)

My book stated this. I am confused to how they did it. Help.

Thanks.

Guest Aug 2, 2017

Alan · Answer 1 · 2017-08-02T02:47:03

Use L'hopital's rule:

lim_h→0(b^h-1)/h → lim_h→0(b^hlog(b)/1) → b⁰log(b) → log(b)