Ib maths sl antiderivatives
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This document discusses indefinite integrals and anti-derivatives. It explains that the indefinite integral of a function is the set of all anti-derivatives of that function. It provides rules for finding the anti-derivative of a function given its derivative, such as adding 1 to the power and dividing by the new power. Examples are given of using these rules to find the function given its derivative.
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This document provides an introduction to symbolic math in MATLAB. It discusses differentiation and integration of functions using symbolic operators. Differentiation is defined as finding the rate of change of a function with respect to a variable. Integration finds the original function given its derivative. The document provides examples of differentiating and integrating simple functions in MATLAB's symbolic toolbox and exercises for the reader to practice.
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* Recognize graphs of common functions.
* Graph functions using vertical and horizontal shifts.
* Graph functions using reflections about the x-axis and the y-axis.
* Graph functions using compressions and stretches.
* Combine transformations.
Lesson 23: Antiderivatives (slides)
We can define the area of a curved region by a process similar to that by which we determined the slope of a curve: approximation by what we know and a limit.
Lesson 23: Antiderivatives (slides)
At times it is useful to consider a function whose derivative is a given function. We look at the general idea of reversing the differentiation process and its applications to rectilinear motion.
Function in Mathematics
This is about Some features of function,
Variation of Function,
Explain of function,
Interval ,
Domain,
Use of Function
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- Integrals may be used to find the area between two curves by subtracting their integrals between the intersection points.
- Integrals can represent either positive or negative areas depending on whether the area is above or below the x-axis.
antidifferentiation.ppt
This document discusses antiderivatives and indefinite integrals. It begins by explaining that an antiderivative of a function is the original function given its derivative. It then provides examples of using power rules to find antiderivatives. The document notes that indefinite integrals represent families of antiderivatives since a constant can be added. It lists several properties of indefinite integrals including how to integrate sums and differences as well as how constants can be factored out. It concludes by providing practice problems for finding specified indefinite integrals.
Continuity and differentiability
The document discusses key concepts in calculus including continuity, differentiation, integration, and their applications. It defines continuity as being able to draw a function's graph without lifting the pen, and differentiation as computing the rate of change of a dependent variable with respect to changes in the independent variable. The document also covers differentiation rules and techniques for implicit, inverse, exponential, logarithmic, and parametric functions.
Limits and derivatives
The document discusses functions and their derivatives. It defines functions, different types of functions, and notation used for functions. It then covers the concept of limits, theorems on limits, and limits at infinity. The document defines the slope of a tangent line to a curve and increments. It provides definitions and rules for derivatives, including differentiation from first principles and various differentiation rules. It includes examples of finding derivatives using these rules and taking multiple derivatives.
Limits and Continuity - Intuitive Approach part 1
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U1 Cn2 Functions
Functions relate dependent and independent variables, where the dependent variable is determined by the independent variable. Functions can be expressed as equations, tables, or graphs. Even functions are symmetric about the y-axis and odd functions are symmetric about the origin. The domain of a function is the set of valid inputs and the range is the set of outputs. A function can be restricted to only certain domain values or composed of multiple functions.
Maths 12
This document provides an introduction to functions and their key concepts. It defines a function as a rule that assigns each element in one set to a unique element in another set. Functions can be represented graphically and algebraically. Common types of functions discussed include polynomial, linear, constant, rational, trigonometric, inverse trigonometric, exponential, logarithmic, and hyperbolic functions. Examples are provided to illustrate domain, range, and graphing of different function types.
2nd-year-Math-full-Book-PB.pdf
This document provides an introduction to functions and limits. It defines key concepts such as domain, range, and different types of functions including algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and hyperbolic functions. Examples are provided to illustrate how to find the domain and range of functions, evaluate functions, and draw graphs of functions. Function notation and the concept of a function as a rule that assigns each input to a single output are also explained.
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Calculus 1 Lecture Notes (Functions and Their Graphs)
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Ib maths sl antiderivatives
- 1. Anti-derivatives. Indefinite Integrals By the end of this lesson you will be able to: • Understand the integration process as the reverse process of differentiation. • Calculate the integrals of powers of x and any linear combination of them.
- 5. In general:
- 11. ( (