Estimate the given value using linear approximation and without using any kind of computationalaid.

Question

a) ln(1.1)

b)√8.9

c)sec(0.1)

Answer 1

a) ln(1.1) The ln(1) = 0. Based on what we know about the parent function, it increases.This means that the ln(1.1) would be a little bit greater than 0, approximately 0.10

b)√8.9 For this, the √9 = 3. So this would be a little less than 3, around 2.9

c) sec(0.1) Since this is very close to 0, that can be used to approximate. Sec (1) = 1. Based on what we know about the parent function, it increases. So this would be a little more than 1, 1.1 would be an approximation.