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Introductory Calculations I
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Transcript of Introductory Calculations I
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