Differential calculus is a branch of mathematics that deals with the study of rates of change and slopes of curves. It focuses on finding the derivative of a function, which is the instantaneous rate of change of the function at a particular point. The derivative gives us information about the steepness of a curve at…
Let $f(x)$ and $g(x)$ be two functions, and let $c$ be a real number. The sum of the two functions $f(x)$ and $g(x)$ is defined by $(f+g)(x) = f(x) + g(x)$ for all $x$ in the domain of both functions. To determine if the sum of $f(x)$ and $g(x)$ is continuous at $c$, we need…
Continuity is a fundamental concept in calculus that describes how a function behaves at every point in its domain. A function is said to be continuous if it has no abrupt jumps, breaks, or holes in its graph. More formally, a function f(x) is continuous at a point x=a if three conditions are met: If…
The limit of a function at a real number is a fundamental concept in calculus that describes the behavior of a function as the input values approach a specific real number. Formally, we say that the limit of a function f(x) as x approaches a real number c is L if for every ε >…
