32. \( \lim _{x \rightarrow 1}\left(4 x^{3}-6 x+5\right) \)

To find the limit \( \lim _{x \rightarrow 1}\left(4 x^{3}-6 x+5\right) \), we can simply substitute \( x = 1 \) directly into the expression since it's a polynomial and continuous everywhere. Calculating it step-by-step: \[ 4(1)^3 - 6(1) + 5 = 4(1) - 6 + 5 = 4 - 6 + 5 = 3. \] Thus, the limit is \( 3 \).