Show transcribed image text (15 marks) Respecting the real-valued function f(x) where x E R, identify the properties of f(x) corresponding to the following definitions: 1. a. lim x→c f(x) = f(c) for all x f (xt n-r(X) exists for all x c. f'(x) 2 0 for all x or f'(x) s 0 for all x d. f(ta (1-t)b) s tf(a) (1 – t)f(b) for all a and b where t e [0,1] e. f(r)-tkf(x) for all x where t > 0 and k ε R
(15 marks) Respecting the real-valued function f(x) where x E R, identify the properties of f(x) corresponding to the following definitions: 1. a. lim x→c f(x) = f(c) for all x f (xt n-r(X) exists for all x c. f'(x) 2 0 for all x or f'(x) s 0 for all x d. f(ta (1-t)b) s tf(a) (1 – t)f(b) for all a and b where t e [0,1] e. f(r)-tkf(x) for all x where t > 0 and k ε R
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