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2. Prove by induction that n n(n + 1)(2n + 1) lim ? 6. Evolueto the not oron hotwoon the curvo flo) - 1 23 ond th ||

2. Prove by induction that n n(n + 1)(2n + 1) lim ? 6. Evolueto the not oron hotwoon the curvo flo) - 1 23 ond th ||

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Given that f (x) = x – 2 sin 2.x, estimate f(x) dx by calculating the right endpoints of of Riemann sum R6. 2. Prove by induction that n(n + 1)(2n + 1) lim i? : 6. i=1 3. Evaluate the net area between the curve f(x) = 1+2.x3 and the x-axis for 0 <x < 5 using the Riemann sum definition of the definite integral, given that n n2(n + 1)2 lim b = bn and lim )3: %3D 4 i=1 i=1
Transcribed Image Text:1. Given that f (x) = x – 2 sin 2.x, estimate f(x) dx by calculating the right endpoints of of Riemann sum R6. 2. Prove by induction that n(n + 1)(2n + 1) lim i? : 6. i=1 3. Evaluate the net area between the curve f(x) = 1+2.x3 and the x-axis for 0 <x < 5 using the Riemann sum definition of the definite integral, given that n n2(n + 1)2 lim b = bn and lim )3: %3D 4 i=1 i=1
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