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Unformatted text preview: P (0 , , 0), Q (1 , 2 , 3), R (2 , 3 , 4), S (3 , 5 , 7) 3. (10 points) Consider the function f ( x ) = sin( x ) (a) (5pts) Find the second Taylor polynomial, T 2 ( x ), for f based at b = π/ 2. (b) (5pts) Find an interval J containing b = π/ 2 such that the error,  f ( x )T 2 ( x )  is less than . 01 for all x in J 4. (15 points) Consider the function f ( x ) = Z x e t1 t dt (a) (10pts) Find the Taylor series for f ( x ) based at b = 0 (b) (5pts) Find f (6) (0) 5. (15 points) Let v = h 1 , 3 ,1 i and r = h 1 , 1 , 1 i and consider the line given by, r = r + t v , in vector form. Also consider the plane given by x + 2 y + 2 z + 2 = 0 (a) (5pts) Show that the line and the plane are not parallel (b) (10pts) Find a point on the line at distance 3 from the plane...
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 Spring '07
 Smith
 Math, Taylor Series, Taylor's theorem, student ID number

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