Posted by **Alex** on Monday, December 10, 2012 at 6:18pm.

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.

- math -
**Damon**, Monday, December 10, 2012 at 6:35pm
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

- math -
**Alex**, Monday, December 10, 2012 at 6:42pm
Thank you very much. This problem was giving me too much stress.

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