definition of absolute value

The length of a rod is to be 8.5 cm, with a tolerance of 0.04 cm. Express the tolerance limit as an absolute value inequality. (Use the variable n for the actual measure of the part in cm.) => | n + 8.5 | ≤ 0.04 or | n - 8.5 | ≤ 0.04 or | n - 8.5 | < 0.04 or | n + 8.5 |..

The weight ( w ) of the soccer ball used by the age group 8 to 12, vary from 373 grams to 403 grams, inclusive. Write an absolute value inequality describing the weights of soccer balls that are outside the acceptable range. => | w - 403 | < 373 or | w - 388 | < 15 or | w ..

Evaluate the absolute value expression. | 3 5 | => - 3 5 or - 5 3 or 3 5 or 5 3..

Find the absolute maximum and absolute minimum values for the function f ( x ) = e x (1 + x 2 ) on [- 2, 2]. => 5 e 2 , 1 0 e 3 or 5 e 2 , 5 e 2 or 5 e 2 , 2 e or 5 e 2 , 0 or 0, 5 e 2..

Find the absolute maximum value of f ( x ) = ln ( x 2 + 2 x + 4) on [- 4, 3]. => ln (3) or 3 or ln (19) or 0..

Find the absolute extrema value of f ( x ) = x x 2 + 1 on [0, 3]. => 1, - 2 25 or 1 2 , - 1 2 or 3 10 , 0 or 1 2 , 0 or 0.433, - 0.433..

Find the absolute maximum value of f ( x ) = 20 - 24 x - 15 x 2 - 2 x 3 on [- 5, 3]. => - 241 or 3 or 31 or 15 or 0..

Find the absolute extreme values of f ( t ) = t 2 t 2 + 8 on the interval [-1, 2]. => 0 and - 9 or 1 3 and 0 or 1 3 and 9 or 9 and 0..

Find the absolute maximum value of f ( r ) = 1 - r r 2 + 1 on [- 2, 3]. => 2 or - 3 5 5 or 1 5 or 3 or 0..

Determine the values of x for which the series ∑ n=1 ∞ ( x + 6 ) n n 1 5 5 n converges absolutely. => - 11 < x < - 1 or - 11 ≤ x < 1 or - 11 ≤ x ≤ - 1 or - 6 < x < ∞ or - ∞ < x < ∞..