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m, ne N. (a) You are given that limx→ (x log x) = 0 and that limx→ Use L'Hôpital's rule to show that lim [xm (log x)"] X-0 = m lim [xm (log x)"+¹]. n x→0 Hence, by induction or otherwise, show that lim [xm (log x)"] = 0. X→0 (b) with a reduced power or powers in the integrand. (c) Hence compute ¹x6(log x)5 dx. 1 log x 0. Let Manipulate xm (log x)" dx into an integral of similar form but

m, ne N. (a) You are given that limx→ (x log x) = 0 and that limx→ Use L'Hôpital's rule to show that lim [xm (log x)"] X-0 = m lim [xm (log x)"+¹]. n x→0 Hence, by induction or otherwise, show that lim [xm (log x)"] = 0. X→0 (b) with a reduced power or powers in the integrand. (c) Hence compute ¹x6(log x)5 dx. 1 log x 0. Let Manipulate xm (log x)" dx into an integral of similar form but

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 14EQ
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m, ne N. (a) You are given that limx→ (x log x) = 0 and that limx→ Use L'Hôpital's rule to show that lim [xm (log x)"] X-0 = m lim [xm (log x)"+¹]. n x→0 Hence, by induction or otherwise, show that lim [xm (log x)"] = 0. X→0 (b) with a reduced power or powers in the integrand. (c) Hence compute ¹x6(log x)5 dx. 1 log x 0. Let Manipulate xm (log x)" dx into an integral of similar form but
Transcribed Image Text:m, ne N. (a) You are given that limx→ (x log x) = 0 and that limx→ Use L'Hôpital's rule to show that lim [xm (log x)"] X-0 = m lim [xm (log x)"+¹]. n x→0 Hence, by induction or otherwise, show that lim [xm (log x)"] = 0. X→0 (b) with a reduced power or powers in the integrand. (c) Hence compute ¹x6(log x)5 dx. 1 log x 0. Let Manipulate xm (log x)" dx into an integral of similar form but
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