math
posted by Alex on .
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.

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