Unformatted text preview: + x 2 n1 (2 n1)! , which look similar to ( T 2 n cos)( x ) = ( T 2 n +1 cos)( x ) = 1x 2 2! + x 4 4!x 6 6! + · · · + (1) n x 2 n (2 n )! ( T 2 n1 sin)( x ) = ( T 2 n sin)( x ) = x + x 3 3! + x 5 5!x 7 7! + · · · + (1) n1 x 2 n1 (2 n1)! , So this is strange: except for some diﬀerences in signs at various places, the functions cosh and sinh seem to satisfy a lot of the same identities as cos and sin. Why should these functions, whose deﬁnitions have nothing to do with sine and cosine and whose graphs look nothing like sine and cosine, remind us so much of sine and cosine??? As we’ll see soon in Ma 1a, these mysterious similarities are no coincidence; in fact, they’re an indication that some deeper truth is hiding beneath the surface. .. 1...
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 Fall '08
 Vuletic,M
 Calculus, Exponential Function, Taylor Series, Hyperbolic function, cosh x cosh, Chris Lyons

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