Problem 5 (15%) Assume that φ: R→ R is a function that satisfieswhere a is a real number. Findφ(0). Please justify your answer. Otherwise, you get 0 points.

4. Let G be a simple graph. A path of G is a sequence of distinct vertices v0,v1, Uh such that and are adjacent for each i = 1,2,..., k. The length of the path v0, v1 , ..., is k. The degree of a vertex is the number of edges incident to that vertex. Show that if the minimum degree of G is greater than or equal to k, then G has a path whose length is at least k.

Problem 5 (15%) Assume that φ: R→ R is a function that satisfies

where a is a real number. Findφ(0). Please justify your answer. Otherwise, you get 0 points.

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