4) \( \lim _{x \rightarrow 1} \frac{x^{4}-1}{x-1} \)

Step 1 ：\( \lim_{x \rightarrow 1} \frac{x^{4}-1}{x-1} \) = \( \lim_{x \rightarrow 1} \frac{(x^2+1)(x^2-1)}{x-1} \)

Step 2 ：\( \lim_{x \rightarrow 1} \left[ (x^2+1) \frac{x^2-1}{x-1} \right] \) = \( \lim_{x \rightarrow 1} \left[ (x^2+1) (x+1) \right] \)

Step 3 ：\( \lim_{x \rightarrow 1} \left[ (1^2+1) (1+1) \right] = \( 2(2) \) = 4