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Extreme Value Theorem : Assume that f ( x ) is continuous on the interval [a,b] then there are two numbers a ≤ c, d ≤ b so that f (c ) is an absolute maximum for the function and
More Optimization Problems Example A window is being built in which the bottom is rectangle and the top is a semicircle. If there framing materials is 12 meters what have
On dividing the polynomial 4x 4 - 5x 3 - 39x 2 - 46x - 2 by the polynomial g(x) the quotient is x 2 - 3x - 5 and the remainder is -5x + 8.Find the polynomial g(x). (Ans:4 x 2 +
how many words can be formed from letters of word daughter such that word contain 2vowles and 3consonant
Simplify following. Suppose that x, y, & z are positive. √ y 7 Solution In this case the exponent (7) is larger than the index (2) and thus the fir
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The population of the village is 5000. If in a year, the number of males were to increase by 5% and that of a female by 3% annually, the population would grow to 5202 at the end o
Example of quotient rule : Let's now see example on quotient rule. In this, unlike the product rule examples, some of these functions will require the quotient rule to get the de
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