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Unformatted text preview: θ ) = √ 1 + x 2 . Hence, cos arctan( x ) = cos( θ ) = 1 sec( θ ) = 1 √ 1+ x 2 Instead of using trignometric identities like I have done (ugh. ..) you may try to ﬁnd this solution by using a diagram (sigh of relief). 1 5. (2 pts) Find the domain (in interval notation) for the following functions: (a) f ( x ) = e x 1+ e x Since 1 + e x 6 = 0 for all x , the domain is the whole real line. Or (∞ , ∞ ) (b) g ( t ) = √ 13 t We cannot take the square root of a negative number i.e., 13 t ≥ so. .. 13 t ≥ 1 ≥ 3 t ln(1) ≥ ln(3 t ) ≥ t ln(3) ≥ t Thus, the doman is (∞ , 0] 2...
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 Fall '08
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 Calculus, Geometry, Complex number, 1 pt, 3 pts, 2 pts

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