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Math571. 3th Homework. Due Tuesday, March 6, 2007. 1. Define f : [0, 1] IR by
 

Summary: Math­571. 3­th Homework. Due Tuesday, March 6, 2007.
1. Define f : [0, 1] IR by
f(x) =



x2
sin 1
x2 if 0 < x 1,
0 if x = 0.
Show that f is continuous in [0, 1] and differentiable in (0, 1). Show that
1
0
f (x) dx
does not exists.
2. Let f : [0, 1] IR be the function defined by
f(x) =



  

Source: Arcones, Miguel A. - Department of Mathematical Sciences, State University of New York at Binghamton

 

Collections: Mathematics