ITA200Y5 Lecture : Le preposizioni

Let b > 0 and f : [0, b] → R be continuous and f(b) = 0. Assume that f is differentiable on (0, b). Show: For every n ∈ N, there exists some c ∈ (0, b) such that cf ′(c) = −nf(c).

Hint: Apply Rolle’s theorem to the function g(x) = xⁿ f(x).

What is Δn for the following equation in relating K_c to K_p?

N₂(g) + 3 F ₂(g) ↔ 2 NF ₃(g)

What is Δn for the following equation in relating K_c to K_p?

N₂(g) + 3 F ₂(g) ↔ 2 NF ₃(g)

5. Let f: A + B be a function. (a) Prove that for any two sets C, DCA, we have f( C D) SfCn f(D). (b) Give an example of a function f, and sets C, D, for which f(COD) + f(C)nf(D)