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trp1
@trp1
July 2022
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Вычислите предел, выручите ребята
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srzontmp
Неопределенность 0/0 - вычисляете по правилу Лопиталя lim(x->0)(f(x)/g(x) = lim(x->0)(f '(x)/g '(x))
f(x) = 2^x - 1 f '(x) = 2^x*ln2
g(x) = ln(1+2x) g ' (x) =2/(1+2x)
lim(x->0)((ln2)*2^x)/(2/1+2x) = lim(x->0)(ln2)*(2^x)/2 + 0 =
ln2/2
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Answers & Comments
f(x) = 2^x - 1 f '(x) = 2^x*ln2
g(x) = ln(1+2x) g ' (x) =2/(1+2x)
lim(x->0)((ln2)*2^x)/(2/1+2x) = lim(x->0)(ln2)*(2^x)/2 + 0 =
ln2/2