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(i) Use the Intermediate Value Theorem to prove that there is a number c such that...

(i) Use the Intermediate Value Theorem to prove that there is a number c such that 0 < c < 1 and cos (sqrt c) = e^c- 2.

(ii) Let f be any continuous function with domain [0; 1] such that 0smaller than and equal to f(x) smaller than and equal to 1 for all x in the domain. Use the Intermediate Value Theorem to explain why there must be a number c in [0; 1] such that f(c) =c

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