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PK Ó˜B> METAINF/PK Ó˜B>o9’ GG METAINF/MANIFESTMFManifestVersion 10 CreatedBy 160_24 (Sun Microsystems Inc) PK ʘB> javax/jnlp/PK ʘB>“œ*G. LAUDATO_SIBUŽYRUŽYSBOOKMOBI Î À)˜ / 4v 9Ê ?. Problem 3 Let f 0,1) !R be defined as f (x) ˘ 0 if 0 • x • 1/2 and f (x) ˘ 1 if 1/2 •x ˙1 Show that the function F(x) ˘ Z x 0 f (t)dt, defined for 0 •x ˙1, is differentiable for x 6˘1/2 and is not differentiable for x ˘1/2 Solution f is continuous except at x ˘1/2 By Theorem 6, this means that F is differen tiable everywhere except possibly at x ˘1/2, and F0(x.

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