Ejercicios Resueltos de Límites y Derivadas PDF - Recta Tangente y Más

Calculating Limits and Derivatives

This section delves deeper into limit calculations and introduces derivative problems. Students are asked to compute limits using techniques such as rationalization and to derive equations involving exponential and trigonometric functions.

Definition: Derivative - The rate of change of a function with respect to a variable, typically denoted as f'(x).

Highlight: The page includes a problem on finding the derivative of a composite function: f(x) = e²ˣ · tan(3x), which requires the application of the chain rule and product rule.

Detailed Solutions

This page provides comprehensive solutions to the limit and derivative problems presented earlier. It demonstrates step-by-step approaches to solving complex limits, including the use of L'Hôpital's rule for indeterminate forms.

Highlight: The solution for lim arctan((2x² - 6x) / (x - 3)) as x approaches 3 is particularly noteworthy, showing the application of limit properties to simplify a complex expression.

Example: The derivative of g(x) = √(√x + 1) is calculated using the chain rule, demonstrating how to handle nested square roots.