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Unformatted text preview: | x | . (iv) f ( x ) =-3 (-x ) ( ix ) f ( x ) = 2-log(2-x ). (v) f ( x ) = ln( x + 2). 6. Find the numerical value of: (i) sinh 0 ( v ) sinh(ln 2). (ii) cosh 0 ( vi ) cosh(ln 3). (iii) tanh 0 ( vii ) cosh-1 (1). (iv) tanh 1 ( viii ) sinh-1 (1). 7. Starting from the deﬁnition, prove that: (i) sinh(-x ) =-sinh x . (ii) cosh(-x ) = cosh x . (iii) cosh x + sinh x = e x . (iv) cosh x-sinh x = e-x . (v) cosh( x + y ) = cosh x cosh y + sinh x sinh y . (vi) tanh(ln x ) = x 2-1 x 2 +1 . (vii) 1+tanh x 1-tanh x = e 2 x . 8. If sinh( x ) = 3 4 , ﬁnd the values of the other hyperbolic functions at x . 2...
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This note was uploaded on 01/08/2010 for the course MATH Math103 taught by Professor Dr.prof.mostafaamer during the Winter '09 term at German University in Cairo.
- Winter '09