8th letter of the basic Latin alphabet
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And also, how do you differentiate from the pronunciation of the letter A, if they are similar?
I'm trying to understand the derivative of exponentials. I can make sense of (ax)' = ln(a) ax using l'hopitals and chain rule. I can't understand why lim h->0 (ah - 1)/h becomes ln(a) though
I tried googling and I found this thread https://www.reddit.com/r/learnmath/comments/1oxe65/why_is_lim_h_0_ah_1h_lna/
lim h->0 (ah - 1)/h
= lim h->0 (e ^ (h * ln(a)) - 1)/h
= ln(a) * lim h->0 (e ^ (h * ln(a)) - 1)/(h * ln(a))
= ln(a) * lim (h * ln(a))->0 (eh * ln(a) - 1)/(h * ln(a))
= ln(a)
or http://imgur.com/a/SHgzG
I don't understand the third line.
ln(a) * lim (h * ln(a))->0 (eh * ln(a) - 1)/(h * ln(a))
how does h->0 become (h*ln(a))->0
?
I'm also assuming that lim (h * ln(a))->0 (eh * ln(a) - 1)/(h * ln(a)) becomes 1 so that ln(a) * lim (h * ln(a))->0 (eh * ln(a) - 1)/(h * ln(a)) = ln(a) * 1