Find the limit. Use l'Hospital's Rule where appropriate. If there is a more e $$ \lim_{t \to 0} \frac{e^{4t} - 1}{\sin(t)} $$
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Substitute $t=0$ into the expression: $$ \frac{e^{4(0)} - 1}{\sin(0)} = \frac{e^0 - 1}{0} = \frac{1 - 1}{0} = \frac{0}{0} $$ Since we have the indeterminate form $\frac{0}{0}$, we can apply L'Hôpital's Rule. Show more…
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