Limits and an Introduction to Calculus

In mathematics, limits are used to understand the behavior of a function as it nears a specific value. They are fundamental in establishing the concepts of continuity, derivatives, and integrals. Conversely, calculus is a specific field within mathematics that examines change and movement. It employs ideas such as limits, derivatives, and integrals to find solutions to issues in fields as diverse as physics, engineering, and economics.

Evaluating Limits Approaching a Value

Evaluate the limit: \( \lim_{x \to 2} \frac{4x^2 - 16}{x-2} \).

Evaluating Limits Approaching Infinity

Evaluate the limit as x approaches infinity for the function \(f(x) = \frac{4x^2 - 2x + 1}{6x^2 + 3x - 2}\)