Math  /  Calculus

QuestionCompute the following limit. limh0e5h13h\lim _{h \rightarrow 0} \frac{e^{5 h}-1}{3 h} limh0e5h13h=\lim _{h \rightarrow 0} \frac{e^{5 h}-1}{3 h}= \square (Type an integer or a simplified fraction.)

Studdy Solution
Now apply the limit property limx0ex1x=1\lim_{x \to 0} \frac{e^x - 1}{x} = 1:
limh0e5h15h=1\lim_{h \to 0} \frac{e^{5h} - 1}{5h} = 1
Thus, the expression becomes:
1351=53\frac{1}{3} \cdot 5 \cdot 1 = \frac{5}{3}
The value of the limit is:
53\boxed{\frac{5}{3}}

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