(b) Assume thatgis continuous everywhere. Show thatg+(x) (the positive part ofg(x)) is also continuous everywhere.(c) Express the maximum ofxandyusing the positive part function.Use thatto show that iffandgare continuous functions then the functionh(x) =max(f(x), g(x)) is also continuous.14. Show that the equationx3= sin(x2) + cos(4x+ 3) has at least one solution.15. Show that the functionx-tanxhas infinitely many zeros.16. The functionfis continuous on [0,∞) and limx→∞f(x) = 12. Show thatfis boundedon [0,∞).Ask for help if you think you need itIf you are having trouble with certain type of problems or concepts then you should ask forhelp. Come to one of my or Jo’s office hours and ask questions! If you think you may havetrouble solving problems with a time limit then collect a couple (say five) problems similarto homework problems and try solving them in 90 minutes (with the solutions written upneatly). Remember that it is almost as important that you can present your solutions clearlyas it is to actually find those solutions.GOOD LUCK!3
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