The expression in the image appears to involve the limit:

$\lim_{x \to 2} (1 - x) \tan\left(\frac{\pi x}{4}\right).$

Solution:

1. Substitute $x = 2$: Substituting $x = 2$ into the expression gives: $(1 - 2) \tan\left(\frac{\pi \cdot 2}{4}\right).$

2. Simplify the trigonometric part: $\tan\left(\frac{\pi \cdot 2}{4}\right) = \tan\left(\frac{\pi}{2}\right).$ However, $\tan\left(\frac{\pi}{2}\right)$ is undefined because the tangent function has vertical asymptotes at odd multiples of $\frac{\pi}{2}$.

3. Analysis of the behavior near $x = 2$: As $x \to 2$, the term $1 - x$ approaches $-1$, and the tangent term $\tan\left(\frac{\pi x}{4}\right)$ grows without bound (approaching $+\infty$ or $-\infty$) due to the vertical asymptote of the tangent function.

4. Conclusion: The limit does not exist because the tangent function becomes unbounded as $x \to 2$.

Let me know if you'd like further clarification or additional examples. Here are some follow-up questions to deepen understanding:

1. Why is the tangent function undefined at $\frac{\pi}{2}$?
2. How can we analyze the behavior of limits involving undefined trigonometric functions?
3. What techniques can we use to determine whether limits exist near vertical asymptotes?
4. How would this limit change if $x$ approached a value where $\tan$ is defined, such as $\pi/4$?
5. Can l’Hôpital’s Rule help in solving limits with undefined terms?

Tip: Always analyze the domain of the function and its behavior near points of discontinuity when solving limits.