The maximum and minimum values of a function refer to the largest and smallest values that the function takes on, respectively. To find the maximum and minimum values of a function, we can use the following steps: It’s important to note that a function may not have a maximum or minimum value if it is…
The inverse trigonometric functions are a set of functions that allow us to find the angle or angles associated with a given trigonometric ratio (sine, cosine, tangent, etc.). They are denoted by the prefix “arc” or “inverse” and the abbreviation of the trigonometric function, for example: For example, if we want to find the angle…
The derivative of a polynomial is obtained by differentiating each term of the polynomial with respect to the variable. For example, let’s consider the polynomial: f(x) = 5x^3 + 2x^2 – 7x + 4 To find its derivative, we differentiate each term with respect to x: f'(x) = (d/dx)(5x^3) + (d/dx)(2x^2) – (d/dx)(7x) + (d/dx)(4)…
The continuity of composite functions is governed by the following theorem: Let f be a function defined on an interval I containing a point a, and let g be a function defined on an interval J containing f(a). If f is continuous at a and g is continuous at f(a), then the composite function g…
L’Hôpital’s rule is a technique used to evaluate limits of functions of the form “f(x)/g(x)” where both f(x) and g(x) approach zero (or infinity) as x approaches a particular value. The rule states that if the limit of the quotient of the derivatives of f(x) and g(x) exists, then this limit is equal to the…
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 >…
