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# For f x x name the type of function and describe each of the three transformations from the

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er-example (if false). (a) If |f | is integrable on [a, b], then f is also integrable on [a, b]. (b) If f = F ′ for some function F on [a, b], then f is continuous on [a, b]. (c) If g is continuous on [a,b], then g = G′ for some G on [a,b]. (d) If G(x) = ???? x g is differentiable at p ∈ (a, b), then g is continuous at p.
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lve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax. Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. Let f be a twice-differentiable function such that f′(2)=0 . The second derivative of f is given by f′′(x)=x2e2−x−1 for 0≤x≤6 . (a) On what open intervals contained in 0 View More

Determine f (8) and justify the value.
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properties: f is differentiable everywhere f(x+y)=f(x)f(y) f(0) doesn't equal 0 f'(0) = 1 Show that f(0)=1 Show that f(x) > 0 Use the limit definition of a derivative to show that f'(x) = f(x) for all values of x
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1 ? (Without using differentiation rules) For each statement, explain why it must be true, or use an example to show that it can be false. a)If y = f ( x ) has a horizontal tangent line at x = 1 then y = g ( x ) , where g ( x ) = f ( x − 1 ) + 1 , has a horizontal tangent line at x = 2 . b)A tangent line always has exactly one point in common with the graph of the function.
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ave a horizontal tangent line at x = 1 ? (Without using differentiation rules) For each statement, explain why it must be true, or use an example to show that it can be false. a)If y = f ( x ) has a horizontal tangent line at x = 1 then y = g ( x ) , where g ( x ) = f ( x − 1 ) + 1 , has a horizontal tangent line at x = 2 . b)A tangent line always has exactly one point in common with the graph of the function.
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics