Concept explanations with solved examples for integrals, derivatives, and limits
Explore the fundamental concepts of limits and their application in calculus.
Limits describe the value that a function approaches as the input approaches some point. Understanding limits is key to defining derivatives and integrals.
Example: Evaluate limₓ→2 (x² - 4) / (x - 2) = 4.
Learn the rules of differentiation and how to apply them to solve problems efficiently.
Derivatives represent the rate of change of a function. Master the power, product, quotient, and chain rules to handle any differentiation problem.
Example: Differentiate y = (3x² + 5x)² using the chain rule.
Understand definite and indefinite integrals, substitution, and integration by parts with examples.
Integrals help calculate areas under curves and accumulate quantities. Learn substitution and integration by parts for solving complex integrals.
Example: Evaluate ∫ x e^x dx using integration by parts.