If a function has more than one independent variables, e.g. y = f(x,z), then the change...
If a function has more than one independent variables, e.g. y = f(x,z), then the change in y is generalized to Ay= 4x + Az where the partial derivative oy is the derivative of y with respect tox treating all other independent variables (in this case z) as constant. Example: The area of a rectangle is A = LW. The two independent variables are the length Land width W of a rectangle. Then the average area is Aav = Lay Wav while the error in the area is AA – OL AL + WAW The partial derivative with respect to L keeping W constant is A = ZW) = wal = W Similarly A = UW = L = 1 So the error in the area is AA – MA AL + SA AW = WAL+LAW Let's put in some numbers. What is the area of a rectangle whose length and width are L = 2.6 + 0.1 and W = 2.0+ 0.1? The average area is Aav = La Wav = 2.6 2.0) = 5.2 The error in the area is AA WAL+LAW = 2.0 (+0.1) +2.6 (+0.1) = 0.46 = 0.5 So the area of the rectangle is A = 5.2 +0.5. Question: What is the volume of a cone, V = arh, if r = 3.5+ 0.1 and h = 2.8 + 0.1? Answer must have correct significant figures and precision. Answer: