Pls answer 1a,1b,1c.Let f be an increasing, continuous and differentiable function on R and let g(x) = f(x) = f(x - 1). Suppose that there is m> 0 such that f'(x) > m, for all x E R. Show that Eg(n) diverge. - Hint: Note that since f is increasing, then g(x) > 0. Let sn= g(1) + g(2) + ... + g(n). We need to show that s → +∞o as n → +∞o. a. Show that Sn = f(n) - f(0). b. Apply Mean-Value Theorem to show that there is cn E (0, n) such that Sn = n f'(cn). c. Apply (b) to show that sn→ +∞o as n → +∞. Let f be an increasing, continuous and differentiable function onR and let g(x) = f(x) = f(x - 1). Suppose that there is m> 0 such thatf'(x) > m, for all x E R. Show that Eg(n) diverge.-Hint: Note that since f is increasing, then g(x) > 0. Let sn= g(1) + g(2) +... + g(n). We need to show that s → +∞ as n → +∞o.a. Show that Sn = : f(n) - f(0).b. Apply Mean-Value Theorem to show that there is cn E (0, n) such thatSn = n f'(cn).c. Apply (b) to show that sn→ +∞o as n → +∞.

It is given that f is increasing, continuous and differentiable such that gx=fx-fx-1. To show that…

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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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Pls answer 1a,1b,1c. Let f be an increasing, continuous and differentiable function on R and let g(x) = f(x) = f(x - 1). Suppose that there is m> 0 such that f'(x) > m, for all x E R. Show that Eg(n) diverge. - Hint: Note that since f is increasing, then g(x) > 0. Let sn= g(1) + g(2) + ... + g(n). We need to show that s → +∞o as n → +∞o. a. Show that Sn = f(n) - f(0). b. Apply Mean-Value Theorem to show that there is cn E (0, n) such that Sn = n f'(cn). c. Apply (b) to show that sn→ +∞o as n → +∞.