MTH 162 Lecture Notes - Lecture 7: Hyperbolic Function, Trigonometric Functions
Document Summary
Provide a generalization to each of the key terms listed in this section. Hyperbolic sine sinh (x) = ex e x. 2 tanh (x) = sinh (x) cosh (x) ex e x ex + e x csch (x) = 1 sinh (x) n 6= 0 sech (x) = 1 tanh (x) cosh (x) sinh (x) n 6= 0 ex + e x ex e x. Range sinh(x) cosh(x) tanh(x) csch(x) sech(x) tanh(x) ( , 0) (0, ) ( , 0) (0, ) [1, ) ( 1, 1) (0, 1] ( , 0) (0, ) ( , 1) (1, ) Integral d d dx [sinh (u)] = u dx [cosh (u)] = u dx [tanh (u)] = u d d d dx [csch (u)] = u dx [sech (u)] = u d (cosh (u)) (sinh (u)) (cid:0)sech2 (u)(cid:1) (csch (u)coth (u)) (sech (u)tanh (u)) sinh(x) cosh(x) tanh(x) csch(x) sech(x) coth(x) dx [coth (u)] = u.
