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Nov 01, 16 · g''(x) = − e−x − (e−x − xe−x) ∴ g''(x) = − 2e−x xe−x Similarly the third derivative g(3)(x) = 2e−x e−x − xe−x ∴ g(3)(x) = 3e−x − xe−x So it looks like clear pattern is forming, but let us just check by looking at the fourth derivative;I a d b w p b f f u t o a t b y e g m e f c x i o a v l i f l p z e c n e g i l l e t n i y r s j n o f f i c e r r u x r a c k e t e e r i n g t u b r o t c e r i d z g j m f k b q t l u p u u n e x f k h i r agent badge bank robbery bureau criminal director fbi academy file fraud intelligence investigation j edgar hoover justiceNov 04, 15 · The limit is less than 1, independent of the value of x It follows that the series converges for all x That is, the interval of convergence is −∞ < x < ∞ Actually the sum is equal to the exponential function Σ xn n!



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