Each of the following statements have an assigned value to it. You are to determine whether the statement is true or false. Each statement has a value assigned to it, which happens to be the powers of $2^n$ , where $n$ is the statement number. The sum of values associated with the true statements, can be expressed as $ABC$ . Evaluate $4A + B - 3C$ .

I. All continuous functions are integrable, where defined.

II. All integrable functions are differentiable, where defined.

III. All differentiable functions are integrable, where defined.

IV. All functions that have a finite surface area must have a finite volume. Do not consider any degenerate figures or special cases of a three dimensional function.

V. All functions that have an infinite surface area must have an infinite volume. Do not consider any degenerate figures or special cases of a three dimensional function.

VI. A functions whose integral diverges must have a discontinuity or an asymptote on its graph.

VII. A function whose integral diverges will also have its summation diverge, where defined.

VIII. A function of x, whose improper integral converges can be shifted to the right by a factor of a/x, where a > 0, and will still converge, so long as it has the same bounds as the original integral.

IX. A summation and a definite integral operator can always be interchanged.

X. A differential operator and a definite integral operator can always be interchanged.

The answer is 10.

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Statements, I, III, IV, and VIII are true, therefore we add 2 + 8 + 16 + 256 to obtain 282 as ABC, and so, 4A + B - 3C = 10.