Question

determine the limit. enter dne if it does not exist. $lim_{x
ightarrow10}left(cosleft(\frac{pi x}{5}
ight)
ight)^{\frac{1}{x - 10}}$. attempt 1: 2 attempts remaining. submit answer next item

Explanation:

Step1: Substitute \(x = 10\) into the argument of the cosine - function

First, consider the inner - function \(\frac{\pi x}{5}\). When \(x\to10\), \(\frac{\pi x}{5}=\frac{\pi\times10}{5}=2\pi\).

Step2: Evaluate the cosine function

We know that \(\cos(2\pi)=1\). So, \(\lim_{x\to10}\cos(\frac{\pi x}{5})=\cos(2\pi) = 1\).

Answer:

1