2.5.9 picking out the positive or negative parts of a functionThis problem can be solved using the max,min functions as suggested in the back of the book, or in a more elegant way by simply introducing two piecewise functions on the same footing with the absolute value function, which is 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QyY+SSZQbHVzWEc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JKnBpZWNld2lzZUclKnByb3RlY3RlZEc2JjEiIiE5JEYyMkYyRjFGMUYlRiVGJSIiIj5JJ01pbnVzWEdGJWYqRidGJUYpRiUtRi02JkYwRjFGM0YyRiVGJUYlRjQ=QygtSSVwbG90RzYiNiY3JC1JJlBsdXNYR0YlNiMtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0kieEdGJUYrL0YxOywkSSNQaUdGLiEiJSwkRjUiIiUvSSZjb2xvckdGJTckSSRyZWRHRiVJJWdyYXlHRiUvSSp0aGlja25lc3NHRiU3JCIiIyIiIkZCLUYkNiY3JC1JJ01pbnVzWEdGJUYqRitGMkY5Rj5GQi1GJDYmNyQsJkYoRkJGRiEiIkYrRjJGOUY+RkI=This seems to know when the sin is positive or negative symbolically:QyctSSZldmFsZkclKnByb3RlY3RlZEc2IzckLUkkc2luRzYkRiVJKF9zeXNsaWJHNiI2IyIiJy1GKTYjIiIoIiIiNiQtSSZQbHVzWEdGLDYjRigtRjU2I0YvRjI2JC1JJ01pbnVzWEdGLEY2LUY7Rjg=