(2) Show thatVne-na?lim Vne-na?dalimdrn00for a >0 but not for a = 0.(4) Let f : R → R be a C-function such that f(x) = 0 if and only if x e Z.Suppose the function a : R R satisfies a'(t) =f (x(t)) for all t e R.(a) If Zn{r(t) : t e R} is non-empty, then show that a is constant.(b) If Zn{x(t) : t e R} is the empty set, then show that lim a(t)t+00exists and is an integer.

We have to show that, limn→∞∫α∞ne-nx2dx = ∫α∞limn→∞ne-nx2dx for α>0 but not for α=0.

Answered: (2) Show that Jo for a > 0 but not for…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

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(2) Show that Jo for a > 0 but not for a = 0. lim 818 √ne-na² da a lim √ne-na2 748 da