i heard there is a ratio rule to differentiate, what is it?
134443
Since a ratio is a fraction and a fraction yields a quotient, then I suppose what you call the "ratio rule" is better known to me as the Quotient Rule of Differentiation.\n\nSuppose you have a diffrentiable function that can be described as the quotient of two differentiable function such as\n\nf(x) = u(x)/v(x), \n\nthen \n\nf'(x) = [u'(x)*v(x) - u(x)*v'(x)]/v^2(x).\n\nThe proof is quite straightforward and can be found elementary calculus texts.\n\nOther well-known rules of differentiation are the Product Rule, Power Rule, and Chain Rule.\n\nHowever, if one will learn the underlying meaning of differentiation and not just memorize a bunch of rules, then differential calculus becomes quite intuitive and "simple." Students that memorize rules and formulas in mathematics classes do two things: First, they make the subject far less interesting; and second, they make the subject way too difficult.
65592
its called the "discriminant" and it can be found here:
466101
Just differentiate it. You need f'(x) < 0.\n\nBy the quotient rule, f'(x) = (2x(x^2 + 4) - (x^2)(2x))/(x^2+4)^2.\nNow, since the bottom is a square, thus positive, you just need the numerator to be < 0:\n2x(x^2 + 4) - x^2 * 2x < 0\n2x^3 + 8x - 2x^3 < 0\n8x < 0\nx < 0\nThus it is decreasing on (-∞,0).
146697
The ratio test is a test for a series, basically to determine wether or not it converges. Roughly speak it looks at the ratio of two successive terms and determines wether this tends to zero (i.e. the series converges)\n\nHeres a complete guide to using it
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|t - 78.3| ≤ 38.3\n\nSo either t -78.3 ≤ 38.3 whence t ≤ 116.6\nOR - (t - 78.3) ≤ 38.3\nwhence - t ≤ - 40 ie 40 ≤ t\n\nSo 40 ≤ t ≤ 116.6
314162
When you're given a ratio, you can find an equivalent ratio by multipying or dividing both elements of the ratio by the same number.  For instance, 3:4 = 6:8 (I multiplied both the 3 and 4 by 2... 3x2=6, 4x2=8).\n\nKeeping that in mind, we want to find a simpler way to write the given ratio, and our strategy here will be to find the lowest common denominator (LCD) of the two fractions, and multiply both fractions by that integer.  (If multiplying a fraction times a non-fraction (the LCD) throws you, write the LCD as a fraction by giving it a denominator of 1.)\n\nSo, all you need to work out is:\n\n(1) what's the LCD of 1/3 and 2/5?\n\n(2) when I multiply 1/3 and 2/5 by that number, what do I get?\n\nGood luck!
385054
c) geometric.  Every term is 1/2 of the prior term.  The ratio is 1/2.
220599
I don't know the rule... I don't even think there is one you jsut divide the fraction and see if it repeats... But to change a decimal into a fraction (if you can round the fraction to the hundreths-the first 2 numbers after the decimal-) but multiply the decimal by onehundred and then try to reduce...
164907
Differentiating sinx gives cos x.\n\nDifferentiating sin[f(x)] gives f'(x)cos[f(x)]\n(The chain rule)\n\nf(x) = 5x\n\nso f'(x) = 5\n\nHence:\n\n5cos(5x)
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This one is a candidate for l'Hopital's rule.  Take the derivative of both numerator and denominator, and the resulting fraction (if not of the form 0/0) will give the limit.  If you get 0/0, do it again.
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There is no hard and fast rule, it varies tremendously by product and sector. A good starting point is to check out your competition, you don't want to discover that you have priced your goods way above your nearest competitor.
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it is C as in use the formula for CI for one sample proprtion from your book(i better get the best answer choice cause this is the fifth one i am answering)\nand the above guy is a moron
460242
let's say its da/dx means that you are taking derivates of a respect to x.
56003
It is the length divided by the radius
423039
Ratio is very easy and I donot think,you should at all worry about it.In fact it is mathematical way of comparing between two things Say your height to your friend's, or no.of apples you have with those of Tracy or to the marks obtined by John with that of Sam etc>Just remember,comparasion can not be done about two things that are not similar and hene ratios are also made of two or more similar quantities.Ratios are expressed in either of the following ways  4:5 (say)or 4/5  or 2:3(or 2/3) or 1:6(or 1/6).The most important thing you should remember is that because ratio is an comparasion between two similar quantity or quality.there is no unit of ratio.\nNow,let us solve the problems quickly\nBrown candies:Green Candies=21;6=7:2 (after dividing both the numbers by 3 to reduce them} and that is your answer.I have tried to explain to you the ratio problems but if you feel that some point/s is/are not clear,please donot hesitate to send me a mail through Yahoo Answers and I shall be too glad to explain the same to you with the best of my abilities.
68875
same as differnce between 1 and 2
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Given:\n7<=3-2p<11\n\nYou want to isolate p, and as long, we only add and subtract its OK as long we do it in every term in the inequality.\n\nOf cause, we want to add -3 in the term in the middle, and therefore in rest of the expression, we get:\n7-3<=3-3-2p<11-3 <=>\n4<-2p<8\nNow we want to divide with 2 and we can do so, as long, we do it in all term, but we also want to multiply with -1, but it's also OK if we remember to reverse the inequality sign. \nThis use to be the point of confusion in calculation with inequalities\nHowever, it is easy to se that it is true\nEx 7<8 multiply with -1 gives\n-7<-8 but that not true therefore we have to reverse the inequality sign, if we multiply with a negative number.\n\nBack on track:\n\n4<=-2p<8<=>\n-4/2=> p >-8/2\n.......NB!!.NB!!!\n -2=>p>-4 \nOr if you better like the result in adequate form\n\nx={ x in R l (-4<p<= -2)}\n================