Question

Find the value of the function y=sqrt(x+1)+sin(x)-0.5, correct to 3 decimal places, when x=0.05 without the use of a calculator.

Answer 1

y = sqrt (x+1) + sin x I assume radians not degrees - .5

= sqrt(1.05) + sin (.05) - .5

first the (1.05)^(1/2)
well if s = t^.5
ds/dt = .5 t^-.5
ds = .5 t^-.5 dt
s (t+dt) = s(t) + .5 dt/sqrt t
here t = 1 and dt = .05
so
sqrt(1.05) = 1 + .5(.05)/1
sqrt(1.05) = 1 + .025 = 1.025

now for small x, sin x = x
so sin .05 = .05

so
1.025 + .05 - .5
= .575

Answer 2

Thank you very much. This problem was giving me too much stress.