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MTH142_Assg03

# MTH142_Assg03 - Assignment 3 Spring 2008 This assignment is...

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Assignment 3, Spring 2008 This assignment is due Monday, February 25, 2008, at the beginning of class. 1. In each problem below, y is deﬁned implicitly by a certain equation. Use implicit di±erentiation to ﬁnd dy/dx. If possible , put your ﬁnal answer in terms of just the variable x . (a) sin y = x. (b) ln y = x ln x. (c) x 2 + y 2 = 1 . (d) ( x + y ) 3 = xy. 2. We deﬁne a certain function cosh( t ) in terms of the variable t as follows: cosh( t ) = 1 2 ( e t + e - t ) . This function is sometimes called the hyperbolic cosine of t . The hyperbolic sine function is similarly deﬁned by sinh( t ) = 1 2 ( e t - e - t ) . Use these deﬁnitions in the following problems. (a) By analogy to the ordinary trig functions, develop formulae for the hyperbolic tangent, hyper- bolic cotangent, hyperbolic secant and hyperbolic cosecant functions. (b) Show that the derivatives of the hyperbolic sine function is the hyperbolic cosine function, and conversely, that the derivative of the hyperbolic cosine is the hyperbolic sine. (c) Compute the derivative of the remaining four hyperbolic trig functions.

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MTH142_Assg03 - Assignment 3 Spring 2008 This assignment is...

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