Use differentials or linearization to approximate the value shown (note each method will give the same result for your chosen x = a). (Round your answer to four decimal places.)

(1.04) ln(1.04)

Question

Use differentials or linearization to approximate the value shown (note each method will give the same result for your chosen x = a). (Round your answer to four decimal places.)
 
(1.04) ln(1.04)

anonymous · Answer

$$\ln(1+x) \approx x$$
1.04 * ln(1.04) ~ 1.04 * 0.04 = 0.0416

anonymous · Answer

Oh, I thought the function would be xlnx

anonymous · Answer

and when I put that in it said it was wrong

anonymous · Answer

1.04 in front  of ln(1.04) is just a constant. You could write it as.
f(x) = x * ln(x) ~ x * (x - 1)
When x ~ 1

anonymous · Answer

Hmm, okay so would I use differentials or linearization ?

anonymous · Answer

Hmm I'm not sure how they teach it in your school / textbook but I think that you actually use both.
The linearization contains the differential. I'm not fully sure, wait for someone else to answer.