If f(x) = 9 cos2(x), compute its differential df. df = (−18cos(x)sin(x))dx correct: your answer is correct. approximate the change in f when x changes from x = π 6 to x = π 6 + 0.1. (round your answer to three decimal places.) δf = .738 incorrect: your answer is incorrect. approximate the relative change in f as x undergoes this change. (round your answer to three decimal places.)

Given: f(x) = 9 cos(2x)

The differential is
df = - 18 sin(2x) dx

When x varies from π/6 to π/6 + 01, then dx = 0.1.
The change in f is
δf = - 18 sin(π/3) *(0.1) = -1.5588 ≈ -1.559

If we compute the change in f directly, we obtain
f(π/6) = 9 cos(π/3) = 4.5
f(π/6 + 0.1) = 9 cos(π/3 + 0.2) = 2.6818
δf = 2.6818- 4.5 = -1.6382 ≈ -1.638

Direct computation of δf is close to the actual value but in error.
The two results will be closer as dx gets smaller.

δf = -1.559  (correct answer)
δf = -1.638 (approximate answer)

Okay so n is going to represent our first number. since the second number of five times greater than n, the second number will be represented as 5n. for us to figure out the two  numbers we need to have  the value of n first. this is going to be done by adding the two numbers together, n and 5n. it can be simplified as 6n, which the problem states is equal to 72. divide 72 by 6n and you can solve for n.  n+5n=726n=72n=(72/6)n=12  now that we know the value of n, we have to multiply 5 times 12 which equals 60. so our two numbers/integers are 12 and 60

020 nanwkwkwkkwkwkwkw