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[DOC File]Topic 4: Differentiation
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Differentiating Exponential Functions (Course Manual, parts of Topic 6.1) Aside: The exponential function: y = exp(x) = ex. Features of y = ex. non-linear. always positive. as ( x get ( y and ( slope of graph. exponential function can be differentiated. Rule 9: If y = ex then where e = 2.71828…. More generally, If y = Aerx then . Examples:
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[DOC File]Integration by Substitution
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Each basic rule of integration that you have studied so far was derived from a corresponding differentiation rule. Even though you have learned all the necessary tools for differentiating exponential, logarithmic, trigonometric, and algebraic functions, your set of tools for integrating these functions is not yet complete.
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[DOC File]Indefinite Integrals Calculus
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8 Integrating Exponential Functions p.54 9 Integrating Exponential Functions p.55-57 (Worksheet) 10 Integrating Rational Functions p.58 11 Integrating Rational Functions p.59-61 (Worksheet) 12 QUIZ 2 13 Riemann Sums p.62-63 (Worksheet) 14 Riemann Sums p.64-65 (Worksheet) 15 Fundamental Theorem of Calculus p.66 16 Definite Integrals p.67 17 ...
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[DOC File]AAA #2 & #3 ( 2 sessions)
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1.5 Exponential Functions - Exponential behavior - exp - Exponential growth and decay - Examples: savings accounts, radioactive decay ... (integrating a DE to find the model: position=f(times)) ... - Integrable and non-integrable functions: examples, integrable => bounded - Properties of definite integrals: rules ...
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[DOC File]IB Diploma programme – HL Mathematics - Summary of ...
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Integrating exponential functions If the base is then . If the base is any other positive number, , then. Integrating and or. When solving differential equations, it is often helpful to replace the constant of integration with another constant in the form , therefore we can use log rules to write
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[DOC File]Mathematics Content Standards K-12
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Provide students examples of Interpreting the number e as a limit and use e to build exponential functions modeling real world applications. Provides students with the opportunity to use common and natural logarithms in the evaluation of logarithmic functions whose base …
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[DOC File]Integration - Teachnet UK
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Integrate trigonometric, exponential functions and . Find volumes of revolution. Find integrals using partial fractions and integrating by parts. Finding solutions to seperable first order differential equations. Find areas under curves and volumes generated from functions given in parametric form.
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[DOC File]Pearson Education
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Examples of such presentations are numerical investigations of limits of functions and their derivatives. ... A summary of the tutorials and projects is given at the end of this introduction to aid in planning a course syllabus integrating this package. ... Tutorial # Title 1 Exponential Functions 2 Differentiation of Exponential Functions 3 ...
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Integrating exponential functions examples