If ρ is mass density, explain why or why not the conservation of mass may be expressed as M = ∫v ρdV For a body of mass M occupying volume V
Answer to relevant QuestionsName the two types of external forces recognized in mechanics and give an example of each.Define when a function f: Rn → R is independent of the first variable and find f1 (a, b) for such f. Which functions are independent of the first variable and also of the second variable?Use the theorems of this section to find f1 for the following: a. f(x, y, z) = xy b. f(x, y) = sin (xsin (y)). c. f(x, y, z) = sin (xsin (ysin (z)) d. f(x, y, z) = xy2 e. f(x, y, z) =xy+z f. f(x, y, z) =(x + ...Find the partial derivatives of the following functions (where g: R →R is continuous): (a) f(x,y ) = fx+ y g (b) f(x,y ) =fx g (c) f(x,y ) =f xy g (d) f(x,y ) =f(fyg)gLet f: Rn →R. For x€ Rn, a. Show that Deif (a) = Dif (a).. b. Show that Dtxf (a) = Dxf(a).. c. If f is differentiable at , show that Dxf(a) = Df(a)(x) (a) and therefore Dx + yf(a) = Dxf (a) + Dyf (a)..
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