Understanding Limits in Calculus: A Comprehensive Guide, Limit Rules and Examples
In calculus, the concept of a limit is fundamental. It describes the behavior of a function as its input approaches…
Category: Calculus
Understanding Continuous and Discontinuous Functions
Continuous Functions Intuitive Idea:A continuous function is one whose graph can be drawn without lifting your pen from the paper.…
Derivatives Explained: Key Rules, Examples and Applications
In mathematics, particularly in calculus, the derivative is a fundamental concept that measures how a function’s output value changes with…
Understanding Maximum, Minimum Values, slope and stationary points
“Maximum” and “minimum” are terms used to describe the highest and lowest possible values of something. Some real-life examples of…
Intro to Taylor Expansion for Multivariable Functions with examples
What is a Taylor Expansion? The Taylor expansion is a way to represent a function (or a multivariable function) as…
Understanding the Jacobian Matrix: a step by step introduction with examples
Ma tr?n Jacobian là công c? trong gi?i tích ?a bi?n, mô t? ??o hàm riêng c?a hàm s?.
Vector derivatives
??o hàm theo vector bao g?m gradient, ma tr?n Jacobian và ??o hàm c?a ma tr?n, ?óng vai trò quan tr?ng trong gi?i tích, t?i ?u hóa và ?ng d?ng trong h?c máy.
Riemann sum
A Riemann sum is a method used in calculus to approximate the integral (or area under a curve) of a function. It is named after the German mathematician Bernhard Riemann. The basic idea behind a Riemann sum is to break up the region under a curve into small rectangles, compute the area of each rectangle, and then sum those areas to approximate the total area under the curve.
Integral: How to weight an elephant?
L??ng Th? Vinh, a renowned scholar, ingeniously weighed an elephant by using water displacement, showcasing his mathematical brilliance. His method relates to integration, which sums small quantities to determine total weight, underlying the connection between math and practical problem-solving.
Calculus can hurt
Supplementary contents for section “Calculus can hurt” in the KSML app: Limit: Derivatives Integral