Given a function f with the following properties. (i)f(x+h) = f(x) + e*f(h) for all real...

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Given a function f with the following properties. (i)f(x+h) = f(x) + e*f(h) for all real numbersx and h (ii)f(x) has a derivative for all real numbers x (iii)if prime (0) = 2 (a) Show that f(0) = 0 (b) Using the definition of f prime (0), find lim as xapproaches 0 of f(x)/x. (c) Prove there exists a real number p such that f(x) = f(x)+ pe* (d) What is the value of the number p that is describedin (c)? Given a function f with the following properties. (i)f(x+h) = f(x) + e*f(h) for all real numbersx and h (ii)f(x) has a derivative for all real numbers x (iii)if prime (0) = 2 (a) Show that f(0) = 0 (b) Using the definition of f prime (0), find lim as xapproaches 0 of f(x)/x. (c) Prove there exists a real number p such that f(x) = f(x)+ pe* (d) What is the value of the number p that is describedin (c)?

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a Show that f00 Since f has a derivative for all real numbers x it is continuous for all real numbers x This means that the limit of fx as x approache... View the full answer