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Unformatted text preview: r < 1 or r > 1. [8] 7. Let f ( x ) = x 3 + x + 1. (a) Show that f ( x ) is invertible. (b) Compute g (3) where g is the inverse function to f . [8] 8. Find all values of x which satisfy the following inequalities. (a) 2 x x1 > 1 (b) 2 x  x1  > 1 MATA26Y page 2 [8] 9. Let f ( x ) =  x1  1. State the hypotheses and conclusion of Rolle’s theorem and explain why this f ( x ) does not contradict the theorem even though f (0) = 0, f (2) = 0, and there is no z in (0 , 2) for which f ( z ) = 0. (You may accept the preceding statement about the derivative of f as fact; you do not have to prove it.) [10] 10. Let f ( x ) = 1 x1 . (a) Find the linear approximation L ( x ) based at x = 3 to f ( x ) . (b) Find an interval (3h, 3+ h ) containing 3 throughout which the error in approximating f ( x )by its linear approximation based at x = 3 is less than 0 . 001....
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This note was uploaded on 03/04/2012 for the course MATH 10250 taught by Professor Himonas during the Fall '08 term at Notre Dame.
 Fall '08
 HIMONAS
 Calculus, Division, Derivative

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