Limits by Algebra: Factoring and Rationalizing Worksheet with Answer Key

What's on the worksheet

1. Evaluate each limit.
   \displaystyle \lim_{x \to 5} \dfrac{x^2 - 2x - 15}{x^2 - 25}\displaystyle \lim_{x \to -2} \dfrac{3x^2 + 5x - 2}{x^2 + 5x + 6}\displaystyle \lim_{x \to 3} \dfrac{x^3 - 27}{x^2 - 2x - 3}\displaystyle \lim_{x \to -3} \dfrac{x^3 + 27}{x^2 + x - 6}\displaystyle \lim_{x \to 2} \dfrac{x^4 - 16}{x^2 - 3x + 2}
2. Evaluate each limit.
3. Expand the numerator, cancel the factor h, and evaluate the limit.
4. Combine the fractions in the numerator, then evaluate each limit.
5. Evaluate the limit below, and explain why multiplying by one conjugate is not enough.
6. Ava evaluates _x -2 x² + 3x + 2x² + 4x + 4.