Find intervals where a function is continuous Identify type of discontinuities

# Find intervals where a function is continuous

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Find intervals where a function is continuous. Identify type of discontinuities a function has. Apply the Intermediate Value Theorem. Determine variable values that make a function have a specific limit or be continuous. Sketch a graph of a function that satisfies given properties regarding limits, continuity, and function values. Use the limit definition of slope of the tangent line to a function to find f ’(a ). Find an equation of the tangent line to a graph at a specific point. State and use the limit definition for the derivative (as a function), f’(x) . Given a graph of a function, sketch the graph of the derivative. Graphically determine where the derivative does not exist: points of discontinuity, sharp corners/cusps, vertical tangent lines. Review exercises: In addition to homework (MyLab Math and uncollected exercises), consider the following questions from the end of Chapters 2 and 3 review. Beginning on page 128, Exercises 1 (a-e and g-h), 2, 4, 5, 8 52, 54 (a, b), 55 60, 66 68, 70 81, 82(a), 83(a), 84, 85(a); Beginning on page 236, Exercises 1(a, d), 2 4, 81, and write equations for tangent lines to the graphs of functions given in 2 4 at some specific point.
• Spring '16
• Derivative, Mathematical analysis, Continuous function, Limit of a function

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