Name: Answer KeyIntroductory Calculations I

Calculate f and its uncertainty. Watch the units, and be sure to show all your work,Use extra piece of paper if necessary.1. Calculate f(x, y) = xy

x = 44.6± 1.6 cmy = 27.35± 0.75 cm

f(x, y) = 1220 cm2

∆f(x, y) =∣∣∣∣∂f

∂x

∣∣∣∣ ∆x +∣∣∣∣∂f

∂y

∣∣∣∣ ∆y

∆f(x, y) = |y|∆x + |x|∆y = 77 cm2

f = 1220± 77 cm2

2. Calculate f(x, z) =z

x

x = 64.2± 1.0 cmz = 21± 2 s

f(x, z) = .33s

cm

∆f(x, z) =∣∣∣∣∂f

∂x

∣∣∣∣ ∆x +∣∣∣∣∂f

∂z

∣∣∣∣ ∆z

∆f(x, z) =∣∣∣ z

x2

∣∣∣ ∆x +∣∣∣∣ 1x

∣∣∣∣ ∆z

∆f(x, z) = .04s

cm

f = .33± .04s

cm

3. Calculate f(x, y, z) =x− y

z

x = 24.5± 7.1 cmy = 1.15± .03 m = 115± 3 cmz = 17.45± 2.5 s

f(x, y, z) = −5.19cms

∆f(x, y, z) =∣∣∣∣∂f

∂x

∣∣∣∣ ∆x +∣∣∣∣∂f

∂y

∣∣∣∣ ∆y +∣∣∣∣∂f

∂z

∣∣∣∣ ∆z

∆f(x, y, z) =∣∣∣∣1z

∣∣∣∣ ∆x +∣∣∣∣−1

z

∣∣∣∣ ∆y +∣∣∣∣y − x

z2

∣∣∣∣ ∆z

∆f(x, y, z) = 1cms

f = −5.19± 1 cms

4. Calculate f(x, y, z) = x2 − yz

x = 25.3± 1.6 cmy = 10.35± 0.05 cmz = 24.2± 1.3 cm

f(x, y, z) = 389 cm2

∆f(x, y, z) =∣∣∣∣∂f

∂x

∣∣∣∣ ∆x +∣∣∣∣∂f

∂y

∣∣∣∣ ∆y +∣∣∣∣∂f

∂z

∣∣∣∣ ∆z

∆f(x, y, z) = |2x|∆x + |−z|∆y + |−y|∆z

∆f(x, y, z) = 96cm2

f = 389± 96 cm2