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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

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tions gn [0, 1] → R given by
In(x) =
x"
n
Consider the sequence of func-
(a) Show that (gn) converges uniformly on [0, 1] and find g = lim gn.
Show that g is differentiable and compute g'(x) for all r = [0, 1].
(b) Show that (gn) converges pointwise on [0, 1]. Is the convergence uni-
form? Let h= lim gn, and compare h and g'. Are they the same?

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