I am supposed to use the definition of the exponential function to prove that if x is a real number and the modulus of x is less than 1, the modulus of exp(x)-1 is less than or equal to (e-1)*modulus of x, and hence prove that the exponential function is sequentially continuous. I've managed to prove the former using the exponential power series but I don't understand how to 'hence' prove the latter.
Prove that the exponential function is sequentially continuous?
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sequences-and-series
analysis
exponential-function
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1What is your definition of "sequentially continuous"? – 2012-12-08
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0@Peter Tamaroff If the sequence x_n converges to x_0, then f(x_n) will tend to f(x_0) as n tends to infinity. – 2012-12-08