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Let E(x) = ∑∞k=0 xk/k!.
a) Prove that the series defining E(x) converges uniformly on any closed interval [a, b].
b) Prove that
for all a, b ∈ R.
c) Prove that the function y = E(x) satisfies the initial value problem
y -y = 0, y(0 ) = l.
[We shall see in Section 7.4 that E(x) = ex.] |
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