The area of a rectangle with dimensions x and y is A(xy)=xy. Find the differential of this function.
If you measure x=6 and y=10, with a measurement error of +/- 0.16, use the differential to estimate the possible error in the caculated area. (Assume that all expressions are in cm. Do not include units in your answer.)
possible error =
OCW Scholar - Multivariable Calculus
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I go the first part to equal ydx+xdy but idk what to do for the second part
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is this differential equations?
no its multivariable variables
sorry, I have no idea how to do this
its ok thank you
Think of the differential equation as saying the change in A = y times the change in x + x times the change in y.\[\Delta A = y * \Delta x + x * \Delta y.\] Plug your x and y values into their appropriate x and y variables. The change in x could be as much as + or - .16. So plug .16 in delta y and delta x.
\[\Delta A = 10(\Delta 0.16) + 6(\Delta 0.16)\]
There are questions (on psets/exams) later on in the course that use this concept.