Calculus 1 — 16.3: Related Rates: Oil Spill скачать в хорошем качестве

Calculus 1 — 16.3: Related Rates: Oil Spill

An oil spill spreads in a circle at 3 feet per second. How fast is the area growing when the radius reaches 30 feet? This problem walks through the complete related rates method — from assigning variables and writing a relating equation to implicit differentiation with respect to time, substitution, and unit checking. You'll see why plugging in values before differentiating destroys the rate information, and why area grows faster as the spill expands even though the radius grows at a constant speed. Key concepts covered: • Related rates problems — linking two quantities that change over time • Implicit differentiation with respect to time using the chain rule • The formula dA/dt = 2πr · (dr/dt) derived from A = πr² • Why you must differentiate before substituting known values • Unit analysis as an error-detection tool • Why area growth accelerates even with constant radial speed (circumference as the expanding frontier) • The general 5-step related rates procedure applicable to any geometry --- ORIGINAL SOURCE This video is based on content from the following source:    • Calculus 1 Lecture 2.8:  Related Rates   All credit for the original lecture and material belongs to the original creator. ---