activity for understanding limits in calculus

Objective: The student will demonstrate and understanding of the corresponding characteristics of graphs of ƒ and ƒ’ the relationship between the behavior of ƒ and the sign of ƒ’. Key ideas: P102–Exploration1 P99–Derivative P100–Derivative at a point, P101–Notation. Objective: The student will be able to find the slope of a curve at a point, emphasizing points at which there are vertical tangents, and no tangents find the tangent line to a curve at a point and use it for local linear approximation understand the instantaneous rate of change as the limit of average rate of change and approximate rate of change from graphs and tables of values. Key ideas: P90–Slope of a curve at a point, P91–normal line to a curve. Objective: The student will be able to recognize a derivative presented graphically, numerically, and analytically interpret the derivative as an instantaneous rate of change understand the derivative as the limit of the difference quotient and understand the relationship between differentiability and continuity. Key ideas: P79–Continuity at a point P83–IVT Objective: The student will have an intuitive understanding of continuity in terms of limits geometric understanding of graphs of continuous functions and be able to apply the Intermediate Value Theorem to appropriate functions. Key ideas: P70–Horizontal Asymptote, lim x→∞ bounded f(x) x =0 P72–Vertical Asymptote P74–End Model Behavior: 𝑚𝑥+𝑏, 𝑥 2, 1 𝑥, 𝑥 2nd & 3rd reasons limits DNE: vertical asymptote, oscillating behavior.Ħ Continuity as a Property of Functions

Objective: The student will have an understanding asymptotes in terms of graphical behavior be able to describe asymptotic behavior in terms of limits involving infinity and be able to compare relative magnitudes of functions and their rates of change. Key ideas: P61–Properties of Limits P64–1 sided Limits P65–Sandwich Theorem 1st reason limits DNE: limit– ≠ limit+.ĥ Asymptotic and Unbounded Behavior Objective: The student will have an intuitive understanding of the limiting process the ability to calculate limits using algebra, and will be able to estimate limits from graphs or tables of data. Objective: The student will be able to predict and explain local and global behaviors of continuous and piece-wise functions with a special emphasis on exponential, logarithmic, trigomometric and inverse functions.Ĥ Limits of Functions (including one-sided limits) stretches and shifts parent functions: polynomials, exponentials, logarithms, fractional powers, negative powers sin, cos, tan, arctan, |x|.ģ Prerequisites– Analysis of Functions, Graphs, and Limits [Units 1. Objective: The student will be able to use lines with their associated graphs and tabular data to predict behavior of modeled functions.

Activity for understanding limits in calculus