In Exercises 16 estimate using the Linear Approximation or l

In Exercises 1-6, estimate using the Linear Approximation or linearization and use a calculater to compute the error. 8.1^1/3 - 2 625^1/4 - 624^1/4 1/1.02 1/root4.1 - 1/2 squareroot101 5root^33

Solution

(1) (8.1)^1/3 = 2[1+0.1/8]^1/3

                  = 2+ 2.(0.1)/24

                  = 2.008   (replace 24 by 25 to estimate)

calculator value = 2.0083

(2)Approximate the diference by

1/2{1-0.1/4}^0.5

= 0.006125

Calculator value= 0.006135

(3)The difference

= 5[1-1/625]^0.25

=0.002

which agrees with the calculator value

(4) Write this as

10[1+1/100]^0.5

⁼ (approx) 10[1+1/200]

= 10.05

Calculator value = 10.0498

5)1/1.02

=1(1+0.02)

= 1-0.02 (linear approx)

=0.98

Calculator value = 0.98039

(6) (33)^0.2

= 2[1+ 1/32]^0.2

⁼ 2+ 2. (0.2)/32

=2.0125

Calculator value = 2.01234