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Continue Learning about Calculus

How do you know when a fraction is in simplest form?

You know a fraction is in its simplest form when neither the numerator (the number on top) nor the denominator (the number on bottom) have any prime factors in common, in other words, when their GCF is 1.


What is the limit of x-sin x cos x over tan x -x as x tends to zero?

The limit is 2. (Take the deriviative of both the top and bottom [L'Hôpital's rule] and plug zero in.)


How do you make a fraction into its simplest form?

Any fraction can be written in many different ways.For example, 1/2 of a cake is the same amount of cake as 4/8ths, or 8/16ths. 3/4 of 100 dollars is the same as 75/100ths of 100 dollars.We say that 1/2, and 4/8 and 8/16 are equivalent fractions. 3/4 and 75/100 are equivalent too.If you take any fraction and multiply both the top number and the bottom number by the same amount, the fraction means the same as before. It doesn't matter what that amount is, as long as it's the same.This also means that you can divide the top and bottom numbers by the same amount too. 12/18 = 6/9. We divided the top and bottom numbers by 2. But we can divide by 3 as well. 6/9 = 2/3. This is the simplest form we can write the fraction in.So to turn a fraction into its simplest form, you go on dividing the top and bottom numbers by whatever whole number you can until you can't divide any more.90/150 = 9/15 (dividing by 10)9/15 = 3/5 (dividing by 3)So 90/150 in its simplest form is 3/5


What does x squared plus 2x divided by x plus 2 equal?

4


What is the derivative of 1 divided by x?

Find dy/dx of y=1/x. It may be simpler for you to examine the equation y=x^-1. This equation is the exact same as y=1/x. Therefore just multiply -1 by x and subtract 1 from the exponent giving you -x^-2 or y=-(1/x^2). You can also do it through quotient rules. Therefore take the derivative of the top 1 which = 0 and multiply that by the bottom X which will give you 0. Then subtract the derivative of the bottom x this equals 1 and multiply it by the top (1). Put this all over the bottom squared. Which leads to -1/x^2. y=1/x = y=x^-1 = -x^-2 = -(1/x^2)=dy/dx or y=1/x = ((0*x)-(1*1)/x^2 = dy/dx=-1/x^2