Evaluating a limit of a rational function

Published on December 3, 2024

To evaluate the limit, direct substitution results in an indeterminate form (0/0). Factoring the numerator reveals a common factor of (x-3), which cancels with the denominator. Substituting x=3 into the simplified expression yields a final answer of 58.

Question

What is the value of lim⁡x→3x4−9x2+4x−12(x−3)(4−x)?x→3lim(x−3)(4−x)x4−9x2+4x−12?

Answer