# HW 4 Solutions - Assignment 4 Math for Economics I(54...

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Assignment 4, Math for Economics I (54 points) Write neat solutions for the problems below. Show all your work. If you only write the answer with no work, you will not be given any credit. Please do not forget to: Write your name. Staple your homework if you have multiple pages! 1. (3 pts) Find the linearization of f ( x ) = 1 (1 + x ) 4 at a = 0, and use it to estimate 1 (0 . 97) 4 .
2. (7 pts total) (a) (2 pts) Find the linearization of ln( x ) at a = 1. (b) (2 pt) Use this linearization to approximate ln(1 . 03) and ln(1 . 8). Using a calculator, compute ln(1 . 03) and ln(1 . 8). (c) (3 pts) Which approximation of ln( x ) in part (b) was closest to the actual value of ln( x )? Justify why we should have suspected this to be the case even if you hadn’t been able to compare your approximations in part (b) with their actual values.
3. (3 pts) The edge of a cube was measured to be 8 cm, with a maximum possible error of 0 . 5 cm. Use a differential to estimate the maximum possible error in computing the volume of the cube. cm. Compare these errors to the answer you got using differentials).