The computer scientists Richard Conway and David Gries once wrote: The absence of error messages during translation of a computer program is only a necessary and not a sufficient condition for reasonable [program] correctness. Rewrite this statement without using the words necessary or sufficient.

Arecipe calls for 2 2/4 cups of raisins, but julie only has a 1/4 measuring cup. how many 1/4 cups is needed to measure out 2 2/4 cups of raisins?

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).

The least common multiple is the multiple, other than 0, common to sets of multiples.