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The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
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This document discusses differentiating functions involving logarithmic and exponential terms. It covers:
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2. Composite functions involve composing one function with another, written as f(g(x)), where the output of g(x) becomes the input for f(x).
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2) The quotient property, which states that log a (u/v) = log a u – log a v. This allows expanding and condensing logarithmic expressions involving quotients.
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1) The derivative of a constant is 0. The power rule states that when taking the derivative of a term with an x to a power, the power is subtracted by 1 and brought in front of the term.
2) When evaluating a derivative, you take the derivative of the function and plug in a value for x. For example, the derivative of f(x)=x^2 evaluated at x=3 is 2x=6.
3) In business and economics, the derivative is used to find marginal costs, revenues, and profits which provide the change in each per additional unit.
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This document provides instructions on solving quadratic equations using different methods: factoring, extracting square roots, the quadratic formula, and determining the discriminant. It explains that if the product of two terms is zero, one of the terms must be zero. This is used to solve equations by setting each factor equal to zero. Examples are provided to demonstrate solving quadratic equations by factoring, taking the square root of both sides, and using the discriminant to determine the number of solutions.
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Dr. Lauren "Jeneva" Moseley's fall 2013 schedule is available by viewing her Google calendar online at https://www.google.com/calendar/embed?src=jenevamoseley%40gmail.com&ctz=America/New_York. Her contact information includes her email address LMOSELEY@LeeUniversity.edu and phone number 423-614-8283.
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The document discusses various techniques for evaluating indefinite integrals (antiderivatives), including:
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2) Expanding rational or negative exponents before integrating
3) Expanding expressions before integrating term by term
4) Simplifying rational expressions by factoring and canceling before integrating
5) Setting up word problems involving integrals to find related functions like total cost, revenue, distance over time.