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Calculus : Reimann Sum and Limits and Continuity

34) The function f is continuous on the closed interval [1,5] and has values that are given in the table below. If 2 subintervals of equal length are used, what is the midpoint Reimann sum approximation of integral with 5 on top and 1 on bottom f(x)dx?
Please given step by step explaination and answer is 32.

x 1 2 3 4 5
F(x)15 10 9 6 5

33) Let f be the function defiend by:
F(x) = x^2-25/5-5 for x does not equal 5
F(x) = 0 for x=5
Which statement of f is true?
I. lim as x approaches 5 of f(x) exists.
II F(5) exists
III F(x) is continuous at x=5.

Please also tell why also false?

Solution Summary

A reimann sum is investigated and the existence of a function is discussed. The solution is well presented.