d) \( \lim _{x-1} 5 x^{2}-3 x+1 \)

To solve the limit \( \lim_{x \to 1} (5x^2 - 3x + 1) \), you can simply substitute \( x = 1 \) into the polynomial expression. Calculating this gives: \[ 5(1)^2 - 3(1) + 1 = 5 - 3 + 1 = 3. \] Thus, the limit is 3. Now, isn't it interesting how limits in calculus can be so straightforward with polynomial functions? They behave very nicely, and often, you just need to plug in the number directly! For more complex functions, you might need to use techniques like L'Hôpital's rule, factoring, or simplifying the expressions to find the limit. Keep these tools handy in your calculus toolbox for when you encounter indeterminate forms!