Question

Find the increment and differential of each of the following functions for the given values of the

variables and their increments.

𝑦 tan^-1 𝑥𝑦; 𝑥 = 2, 𝑦 = 0.5, ∆𝑥 = −0.05, ∆𝑦 = 0.01

Answer 1

𝑦 tan^-1 𝑥𝑦

𝑥 = 2

𝑦 = 0.5

∆𝑥 = −0.05

∆𝑦 = 0.01

x= 1. 05

y= 0.51

𝑦 tan^-1 𝑥𝑦= 0.51tan^-1 (1.05*0.51)

= 0.51 tan^-0.5355

= 0.55935872^-0.5355

= 1.3649