33 lines
325 B
Markdown
33 lines
325 B
Markdown
#Math #Calculus
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Limit to solve:
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$$
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\lim _{x\to 0} \frac {e^x-1} {x}
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$$
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Let $t = e^x - 1$
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$$
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\lim _{t\to 0} \frac {t} {\ln(t+1)}
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$$
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\lim _{t\to 0} \frac {1} {\frac {1} {t} \ln(1+t)}
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Inverse power log rule
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$$
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\lim _{t\to 0} \frac {1} {\ln(1+t)^{\frac {1} {t}}}
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$$
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Definition of e
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$$
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\frac {1} {\ln e}
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$$
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$$
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1
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$$ |