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7 Notes 5

# 7 Notes 5 - MATH 20C Monday rst midterm MATH 20C Lecture 11...

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MATH 20C - Monday, October 18, 2010: first midterm MATH 20C Lecture 11 - Wednesday, October 20, 2010 Functions of several variables Recall: for a function of 1 variable, we can plot its graph, and the derivative is the slope of the tangent line to the graph. Plotting graphs of functions of 2 variables: examples z = - y, z = 1 - x 2 - y 2 , using slices by the coordinate planes. (derived carefully). Contour map: level curves f ( x, y ) = c. Amounts to slicing the graph by horizontal planes z = c. Showed 2 examples from “real life”: a topographical map, and a temperature map, then did the examples z = - y and z = 1 - x 2 - y 2 . Showed more examples of computer plots ( z = y 2 - x 2 , and another one). Contour map gives some qualitative info about how f varies when we change x, y. (shown an example where increasing x leads f to increase). MATH 20C Lecture 12 - Friday, October 22, 2010 Reviewed countour maps and level curves. Limits By substitution: lim ( x,y ) (0 , 0) 3 x 2 + 2 y - 5 cos(4( x + y )) xy - e x - y = 0 + 0 - 5 0 - 1 = 5 Disclaimer: limits do not always exist! For instance, take lim

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7 Notes 5 - MATH 20C Monday rst midterm MATH 20C Lecture 11...

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