# Question: Suppose a static factor of safety

Suppose a static factor of safety is defined as the ratio of resisting to driving forces, that is, FS = R/D. Show that a factor of safety less than one implies acceleration is impending

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Prove that if f: Rn → Rm is differentiable at a € Rn, then it is continuous at a.Let f : R2 →R be defined by f (x, y) = |xy|. Show that f is not differentiable at 0Define IP: Rn x Rn →R by IP (x, y) = . (a) Find D(IP) (a,b) and (IP)’ (a,b). (b) If f,g: R → Rn are differentiable, and h: R → R is defined by h(t) = , show that hI (a) = Let g1, g2: R2→ R be continuous. Define f: R2→Rby f(x,y) = (a) Show that D2f (x,y) = g2(x,y) (b) How should f be defined so that D1f(x,y) =g1(x,y)? (c) Find a function f: R2→R such that D1f (x,y)=x ...Show that the continuity of D1 f j at a may be eliminated from the hypothesis of Theorem 2-8.Post your question