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- https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Nguyen)/02%3A_Limits/2.02%3A_A_Preview_of_CalculusAs we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in th...As we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in the chapter opener. Two key problems led to the initial formulation of calculus: (1) the tangent problem, or how to determine the slope of a line tangent to a curve at a point; and (2) the area problem, or how to determine the area under a curve.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q1/02%3A_Limits/2.02%3A_A_Preview_of_CalculusAs we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in th...As we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in the chapter opener. Two key problems led to the initial formulation of calculus: (1) the tangent problem, or how to determine the slope of a line tangent to a curve at a point; and (2) the area problem, or how to determine the area under a curve.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/Chapter_2_Limits/2.1%3A_The_Idea_of_LimitsAs the widths of the rectangles become smaller (approach zero), the sums of the areas of the rectangles approach the area between the graph of f(x) and the x-axis over the interval [a,b]. A ta...As the widths of the rectangles become smaller (approach zero), the sums of the areas of the rectangles approach the area between the graph of f(x) and the x-axis over the interval [a,b]. A tangent line to the graph of a function at a point (a,f(a)) is the line that secant lines through (a,f(a)) approach as they are taken through points on the function with x-values that approach a; the slope of the tangent line to a graph at a measures the rate of change of the function at a
- https://math.libretexts.org/Courses/Reedley_College/Calculus_I_(Casteel)/02%3A_Limits/2.01%3A_A_Preview_of_CalculusAs we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in th...As we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in the chapter opener. Two key problems led to the initial formulation of calculus: (1) the tangent problem, or how to determine the slope of a line tangent to a curve at a point; and (2) the area problem, or how to determine the area under a curve.
- https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_hdagnew@ucdavis.edu/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2%2F%2FChapter_2_Limits/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2%2F%2FChapter_2_Limits%2F%2F2.1%3A_The_Idea_of_LimitsAs the widths of the rectangles become smaller (approach zero), the sums of the areas of the rectangles approach the area between the graph of f(x) and the x-axis over the interval [a,b]. A ta...As the widths of the rectangles become smaller (approach zero), the sums of the areas of the rectangles approach the area between the graph of f(x) and the x-axis over the interval [a,b]. A tangent line to the graph of a function at a point (a,f(a)) is the line that secant lines through (a,f(a)) approach as they are taken through points on the function with x-values that approach a; the slope of the tangent line to a graph at a measures the rate of change of the function at a
- https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_I_(Reed)/02%3A_Limits/2.01%3A_A_Preview_of_CalculusAs we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in th...As we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in the chapter opener. Two key problems led to the initial formulation of calculus: (1) the tangent problem, or how to determine the slope of a line tangent to a curve at a point; and (2) the area problem, or how to determine the area under a curve.
- https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_I_(Kravets)/02%3A_Limits/2.01%3A_A_Preview_of_CalculusAs we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in th...As we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in the chapter opener. Two key problems led to the initial formulation of calculus: (1) the tangent problem, or how to determine the slope of a line tangent to a curve at a point; and (2) the area problem, or how to determine the area under a curve.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/03%3A_DeterminantsThis page explains the importance of determinants in square matrices, covering their properties, applications, and geometric interpretations. It discusses their relation to matrix inverses and Cramer'...This page explains the importance of determinants in square matrices, covering their properties, applications, and geometric interpretations. It discusses their relation to matrix inverses and Cramer's Rule, emphasizes the effects of row operations on determinants, and includes examples for clarity. Furthermore, it highlights the geometric interpretation of determinants as volumes, enhancing comprehension of their defining properties and relevance in multivariable calculus.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/01%3A_Differentiation_of_Functions_of_Several_VariablesWhen dealing with a function of more than one independent variable, several questions naturally arise. For example, how do we calculate limits of functions of more than one variable? The definition of...When dealing with a function of more than one independent variable, several questions naturally arise. For example, how do we calculate limits of functions of more than one variable? The definition of derivative we used before involved a limit. Does the new definition of derivative involve limits as well? Do the rules of differentiation apply in this context? Can we find relative extrema of functions using derivatives? All these questions are answered in this chapter.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/01%3A_Differentiation_of_Functions_of_Several_Variables/1.02%3A_Limits_and_ContinuityWe have now examined functions of more than one variable and seen how to graph them. In this section, we see how to take the limit of a function of more than one variable, and what it means for a func...We have now examined functions of more than one variable and seen how to graph them. In this section, we see how to take the limit of a function of more than one variable, and what it means for a function of more than one variable to be continuous at a point in its domain. It turns out these concepts have aspects that just don’t occur with functions of one variable.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/02%3A_Limits/2.01%3A_A_Preview_of_CalculusAs we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in th...As we embark on our study of calculus, we shall see how its development arose from common solutions to practical problems in areas such as engineering physics—like the space travel problem posed in the chapter opener. Two key problems led to the initial formulation of calculus: (1) the tangent problem, or how to determine the slope of a line tangent to a curve at a point; and (2) the area problem, or how to determine the area under a curve.
