Use the rule of inference "If A, and A implies B, then B." to prove the following stateme (a) If an integer n is divisible by 18, then it is divisible by 6. (b) Prove: if f(x) is a polynomial, then it has a power series expansion at x = 2.
Let f(x) and g(x) be two real value functions. Let A be a subset of R. Prove: if f(x) ≥ g(x) for all x € A, then f(x)³ + f(x) ≥ g(x)³ + g(x) for all x € A.
Let x E R. Prove: If x < 5 and x ≥ −3, then (x-6)³ +1 <0.
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