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- 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/City_College_of_San_Francisco/CCSF_Calculus/02%3A_Learning_Limits/2.01%3A_Tangent_Lines_and_VelocityWe begin our exploration of calculus by reconnecting with a topic from our early days in algebra - slope. The concept of slope is fundamentally important in calculus and this section, along with our o...We begin our exploration of calculus by reconnecting with a topic from our early days in algebra - slope. The concept of slope is fundamentally important in calculus and this section, along with our old friend "slope," allows a gentle introduction to a monumentally important subject in mathematics and physics.
- 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/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/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus/02%3A_Linear_and_Quadratic_Functions/2.01%3A_Linear_FunctionsThis section covers linear functions, including their definition, graphing, and interpretation. It explains the slope-intercept form y=mx+b, where m represents the slope and b the y-intercept, and dem...This section covers linear functions, including their definition, graphing, and interpretation. It explains the slope-intercept form y=mx+b, where m represents the slope and b the y-intercept, and demonstrates how to find and interpret these values. It also addresses real-world applications of linear functions, such as modeling and predicting trends. Examples and exercises help reinforce understanding of these key concepts.
- https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/03%3A_Inequalities_and_Functions/3.06%3A_Average_Rate_of_ChangeThe average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values. The average rate of change on this interval, \...The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values. The average rate of change on this interval, \([a,a+h]\), is \[\dfrac{f(a + h) - f(a)}{(a + h) - a}\nonumber\] which is visually the slope of a secant line passing through these two points on the graph of the function, as shown in Figure \(\PageIndex{2}\) below.
- 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.
- https://math.libretexts.org/Courses/Highline_College/MATH_141%3A_Precalculus_I_(2nd_Edition)/02%3A_Inequalities_and_Functions/2.06%3A_Average_Rate_of_ChangeThe average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values. The average rate of change on this interval, \...The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values. The average rate of change on this interval, \([a,a+h]\), is \[\dfrac{f(a + h) - f(a)}{(a + h) - a}\nonumber\] which is visually the slope of a secant line passing through these two points on the graph of the function, as shown in Figure \(\PageIndex{2}\) below.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2410%3A_Calculus_(Open_Stax)_Novick/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/Cosumnes_River_College/Math_370%3A_Precalculus/02%3A_Linear_and_Quadratic_Functions/2.01%3A_Linear_FunctionsWe now begin the study of families of functions. Our first family, linear functions, are old friends as we shall soon see. Recall from Geometry that two distinct points in the plane determine a unique...We now begin the study of families of functions. Our first family, linear functions, are old friends as we shall soon see. Recall from Geometry that two distinct points in the plane determine a unique line containing those points.
