Final Answer
$1808.042414$
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Step-by-step Solution
Problem to solve:
$\lim_{x\to0}\left(\left(1+\frac{5x}{2}\right)^{\frac{3}{x}}\right)$
Specify the solving method
1
Combine $1+\frac{5x}{2}$ in a single fraction
$\lim_{x\to0}\left(\left(\frac{5x+2}{2}\right)^{\frac{3}{x}}\right)$
Learn how to solve limits of exponential functions problems step by step online.
$\lim_{x\to0}\left(\left(\frac{5x+2}{2}\right)^{\frac{3}{x}}\right)$
Learn how to solve limits of exponential functions problems step by step online. Find the limit (x)->(0)lim((1+(5x)/2)^(3/x)). Combine 1+\frac{5x}{2} in a single fraction. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(\frac{5x+2}{2}\right). Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}.
Final Answer
$1808.042414$