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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 -

    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 -

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

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