Hands on Mathematics for CS - News

11. Session: January 19th

Erroneous examples (additional exercise given in Session 9 )

• Steffen Heil, Verena Kremer, Daniel Schmitt
• Michael Dietrich, Dominik Jednoralski

• Sebastian Germesin, Stefan Nesbigall

• Michael Dietrich, Dominik Jednoralski

Continuity:

• Solve the LeAM exercise on continuous functions (only in German available). Make up three new (not in LeAM included) examples for continuous functions and three against. The latter is quite easy, so please provide some tricky ones. (*)
  

• Explain the conection between continuity and differentiability . Provide graphical examples. Where do you suppose comprehension problems? Give also examples for a continuous but not differentiable function. (**)
  

• Show by applying the difference quotient which of the following functions is differentiable. Record each step. Hightlight the key points. Where are the main difficulties. Where are errors possible (source for erroneous examples) Provide a brief exercise diagram that focuses on the key points. (**)
  • f(x)=x²
    

  • f(x)=1/x
    

  • f(x)=|x-1|
    

  • f(x)= √x with x≤4 and f(x)=x/4 + 1 with x>4
  
  

• Write an applet, that draws a 'Steigungsdreieck' for each selected Point x_0 and arbitrary Point x for any function. The value of x can be changed by a slider. The goal is, that the user learns, how the slope changes if x goes to x_0. The value of the difference quotient has to be displayed. (***)