Which of the following statements are correct? Choose all that apply.


a. lim x→1 1/ (x−1)^2 does not exist


b. lim x→1 1/ (x−1)^2=∞


c. lim x→1 1/(x−1)^2=−∞

Key Concepts

Limits

In calculus, a limit describes the behavior of a function as its input approaches a certain value. It helps in understanding how functions behave near points of interest, including points where they may not be defined. Evaluating limits is crucial for determining continuity, derivatives, and integrals.

Infinite Limits

An infinite limit occurs when the value of a function increases or decreases without bound as the input approaches a certain point. For example, if the limit of a function approaches infinity, it indicates that the function's values grow larger and larger, which is essential for understanding vertical asymptotes in rational functions.

Behavior of Rational Functions

Rational functions are ratios of polynomials, and their limits can exhibit unique behaviors near points where the denominator approaches zero. Understanding how these functions behave near such points, including whether they approach positive or negative infinity, is key to solving limit problems and analyzing their graphs.