1) 0.682 2) 3.317 3) -0.489 4) 0.569 5) 0.824 6) a) L ( x ) = 21.6 x − 48.6 b) 16.2216 c) f (3.001) = 16.2216108 error = .0000108

(

7) a) L ( x ) = 2 + 2 3 x −

π 3

)

b) 1.96535 c) g

f (0.02) = 1.030153544 error = 0.000154 9) a)

( π3 − .01) = 1.966 error = 0.000687

dy 16 x − 5 y = dx 5 x + 3 y 2

8) a) L ( x ) = 1 +

3 x b) 1.03 c) 2

3

b) y = 3 x − 13 c) -0.4 d) k + 21k = −7.88 k = -0.373 10) a)

f ( 0.9 ) ≈ 4.8 f (1.2) ≈ 5.4 b) The estimates are too large since f(x) is concave down so the tangent lines lie above the graph of the function, and since L(x) appears to be above the graph of f’(x) which is the actual change of f(x).