Let a and b be real numbers with a < b. Let f : (a, b) → R be Score: /25 points an increasing function. Suppose that f has the intermediate value property: if a < c < d < b and f(c) < τ < f(d), then there is a real number t with c < t < d and with f(t) = τ . Let x ∈ (a, b). Prove that f is continuous at x.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

16

step-by-step explanation: