# Sagetex: Limits

LIMITS OF FUNCTIONS

Problem Type 1: Removable discontinuity from factoring a quadratic.

Problem Type 2: Use $latex \displaystyle\lim_{x \to 0}\frac{\sin(x)}{x}=1$to evaluate a limit.

Problem Type 3: Evaluating a limit which is $latex \infty$ from one direction and $latex -\infty$ from the other direction.

Problem Type 4: Evaluating a limit which is $latex \infty$ from one direction and $latex \infty$ from the other direction.

Problem Type 5: Find the area under a quadratic using limits.

Problem Type 6: Find the derivative of a quadratic using the limit of a difference quotient.

Problem Type 7: Find the limit of a rational function as $latex x \to \infty$.Download file: Limits7  (.tex)

Problem Type 8: Find a limit using the Squeeze Theorem

Problem Type 9: $latex \lim_{x \to -3}\frac{\frac{1}{3}+\frac{1}{x}}{3+x}$

Problem Type 10: $latex \lim_{t \to 0}\left(\frac{1}{t}-\frac{9}{t(t+9)}\right)$

Problem Type 11: Evaluate the limit: $latex \displaystyle \lim_{x \to 1}\frac{x^{7}-1}{x^{3}-1}$
Problem Type 12: Find $latex \displaystyle\lim_{x \to \infty} \ln\left(\frac{5x^7-1}{11x^2-1}\right)$
Problem Type 12b: Find $latex \displaystyle\lim_{x \to \infty} \ln\left(5x^7-1 \right)- \ln\left(11x^2-1\right)$