Graphmatica trig functions
![graphmatica trig functions graphmatica trig functions](https://i.ytimg.com/vi/mBlC4ffAMYA/maxresdefault.jpg)
* Application of definite integrals including area, volume, position/velocity/acceleration and accumulation functions * Antiderivatives and Indefinite Integration * Use of Riemann sums and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically and by tables of values * Finding specific antiderivatives using initial conditions, including applications to motion along a line * Find antiderivatives including the use of substitution * Use of the Fundamental Theorem of Calculus to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined * Use of the Fundamental Theorem of Calculus to evaluate definite integrals * Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval: * Definite integral as a limit of Riemann sums Module 4: Integration Suggested Pace: 4 weeks * Oral Review: Discussion about using the calculator to find the critical values of a function by examining the graph of the function and the graph of the function’s derivative.
![graphmatica trig functions graphmatica trig functions](https://i.ytimg.com/vi/k4M8l_YVegQ/maxresdefault.jpg)
Major Assignments and Assessments * Problem sets * Concavity and the second derivative test * Rolle’s Theorem and the Mean Value Theorem * Optimization – absolute and relative extrema * Analysis of curves including monotonicity and concavity * Mean Value Theorem and geometric consequences * Points of inflection as places where concavity changes * Relationship between the concavity of f and the sign of f’ * Corresponding characteristics of graphs of f, f’, and f’’ * Relationship between the increasing and decreasing behavior of f and the sign of f’ * Corresponding characteristics of graphs of f and f’ * Test – Differentiation Module 3: Applications of Differentiation Suggested Pace: 6 weeks Discussion about the limitations of the calculator to find the numerical derivative (for example, f ‘(0) for f (x) = |x|).
#Graphmatica trig functions how to
* Oral Review: Discussion about using a calculator to find the value of a derivative at a point, and how to graph the derived function using a calculator. * Quiz – Definition and computation of derivatives
![graphmatica trig functions graphmatica trig functions](https://studymaterialcenter.in/wp-content/uploads/2021/05/Inverse-Trigonometric-Function2-scaled.jpg)
* Basic differentiation rules and rates of change * The derivative and the tangent line problem * Modeling rates of change and solving related rates problems * Equations involving derivatives and problems using their verbal descriptions * Chain rule and implicit differentiation * Approximate rate of change from graphs and tables of values * Instantaneous rate of change as the limit of average rate of change * Derivative interpreted as instantaneous rate of change * Basic rules for the derivatives of sums, products, and quotients of functions * Knowledge of derivatives of power and trigonometric functions * Graphic, numeric and analytic interpretations of the derivative * Derivative defined as the limit of the difference quotient * Test – Limits and Continuity Module 2: Differentiation Suggested Pace: 5 weeks * Elluminate Session: Discussion about conditions of continuity. Discussion about the limitation of a graphing calculator to show discontinuities in functions and the value of using a calculator to support conclusions found analytically.
![graphmatica trig functions graphmatica trig functions](https://www.unmisravle.com/wp-content/uploads/2018/07/graphing_trigonometric_functions_worksheet_with_answers_the_best_2.jpg)
* Oral Review: Discussion about using the Calculator to experiment and produce a table of values to examine a function and estimate a limit as x approaches a point and as x grows without bound. * Finding limits graphically and numerically * Understanding graphs of continuous or non-continuous functions geometrically * Understanding continuity in terms of limits * Describing asymptotic behavior in terms of limits involving infinity * Calculating limits using algebraic methods * Intuitive understanding of limit process * Quiz – Functions, Graphs, and Rates of Change Module 1: Limits and Continuity Suggested Pace: 2 weeks * Oral Review: Discussion about using Calculator zoom features to examine a graph in a good viewing window and calculator operations to find the zeros of a graph and the point of intersection of two graphs * Comparing relative magnitudes of functions – contrasting exponential, logarithmic and polynomial growth * Using the Cartesian coordinate system to graph functions * Understanding the properties of real numbers and the number line Major Topics and Concepts Module 0: Preparation for Calculus Suggested Pace: 2 weeks This course includes a study of limits, continuity, differentiation, and integration of algebraic, trigonometric and transcendental functions, and the applications of derivatives and integrals.
#Graphmatica trig functions software
Walk in the footsteps of Newton and Leibnitz! An interactive text and graphing software combine with the exciting on-line course delivery to make Calculus an adventure.