Unformatted text preview: , x ] and that F ′ ( t ) = ( x − t ) n − 1 ( n − 1)! ( f ( n ) ( t ) − M ) . ii) By showing F (0) = F ( x ) and applying Rolle’s theorem 29.2 to F prove that there exists y ∈ (0 , x ) such that f ( n ) ( y ) = M . 3. Let ( S 1 , d 1 ), ( S 2 , d 2 ) and ( S 3 , d 3 ) be metric spaces. Suppose two functions f : S 1 → S 2 and g : S 2 → S 3 are continuous. Show that g ◦ f is continuous by using the de²nition 21.1. 1...
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 Fall '07
 Fukuda
 Calculus, Derivative, Taylor Series, Hyperbolic function, MAT 125A Homework

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