Questions: Find the limit of the transcendental function. lim x→1 cos(πx/3)

Solution Steps

To find the limit of the given transcendental function as $x$ approaches 1, we can directly substitute $x = 1$ into the function, since cosine is continuous everywhere. This will give us the value of the limit.

To find the limit of the function $\lim_{x \rightarrow 1} \cos \left(\frac{\pi x}{3}\right)$, we substitute $x = 1$ into the function. This is possible because the cosine function is continuous everywhere.

Substitute $x = 1$ into the function: $$\cos \left(\frac{\pi \times 1}{3}\right) = \cos \left(\frac{\pi}{3}\right)$$

The value of $\cos \left(\frac{\pi}{3}\right)$ is known to be $\frac{1}{2}$.

Final Answer