Linear Approximation and Differentials
Read this section to learn how linear approximation and differentials are connected. Work through practice problems 1-10.
Practice Problem Answers
Practice 1: so . At the point on the graph of , the slope of the tangent line is . The equation of the tangent line is
Practice 2: so . At , the slope of the tangent line is . The equation of the tangent line is or . Then and .
Practice 5: and so and . Then "error" . When and , "error" .
Finally, "error" so and radians .
Practice 8: so and We are also told that Percentage error is .
is the actual volume of the cube with side length .
is the volume of the cube with side length plus the volume of the 3 "slabs"
is the volume of the "leftover" pieces from : the 3 "rods" and the tiny cube .