T3ReviewProb - 1205 Review Problems Test 3 1.a Find the...

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1205 Review Problems Test 3 1.a) Find the linearization of f ( x ) = x + 3 at x = 1 . (b) Use the linearization in (a) to approximate the value of 3.9 . 2. Find the linearization L ( x ) of the function at a : f ( x ) = x 3 , a = 1 3. Find the linearization L ( x ) of the function at a : f ( x ) = x 3 , a = ! 8 4. (a) Find the differential dy and (b) evaluate dy for the given values of x and dx for y = x 2 + 2 x , x = 3, dx = 1 2 5. (a) Find the differential dy and (b) evaluate dy for the given values of x and dx for y = 1 ! x , x = 0, dx = 0.02 6. Find the absolute maximum and absolute minimum values of f on the given interval: f ( x ) = 3 x 2 ! 12 x + 5, 0,3 [ ] 7. Find the absolute maximum and absolute minimum values of f on the given interval: f ( x ) = x 2 + 2 x , 1 2 ,2 ! " # $ % & 8. Find the absolute maximum and minimum values of f ( x ) = x x 2 + 1 on the closed interval [0,2]. Show all necessary work to justify your answer. 9. Find the third degree Taylor Polynomial, P 3 ( x ) , for the function f ( x ) = ln( x ) centered at x = 1. 10. A spherical balloon of radius 10 inches is inflated so that the volume is increased by 2512 in 3 . Use differentials to estimate the corresponding increase of radius of the balloon. The volume of a sphere is
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