Let f be a continuous and differentiable function on R. Let h: R→ [0, +∞) be a function such that 0≤ f'(a)| ≤h(a) ≤h([a]) Let g(x) = f(x)-f(x - 1). Show that if Eh(n) converge, then g(n) is absolutely converge. Hint: Apply Comparison Test.

Let f be a continuous and differentiable function on R. Let h: R→ [0, +∞) be a function such that 0≤ f'(a)| ≤h(a) ≤h([a]) Let g(x) = f(x)-f(x - 1). Show that if Eh(n) converge, then g(n) is absolutely converge. Hint: Apply Comparison Test.

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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Question

Pls answer. Let f be a continuous and differentiable function on R. Let h: R→ [0, +∞o) be a function such that 0 ≤ f'(a)| ≤h(a) ≤h([a]) Let g(x) = f(x)-f(x - 1). Show that if Eh(n) converge, then Eg(n) is absolutely converge. Hint: Apply Comparison Test.

Let f be a continuous and differentiable function on R. Let
h: R→ [0, +∞o) be a function such that
0 ≤ f'(a)| ≤h(a) ≤ h([a])
Let g(x) = f(x)-f(x - 1). Show that if h(n) converge, then Eg(n) is
absolutely converge.
Hint: Apply Comparison Test.

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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