The remainder is 8. (x2 + 4)/(x - 2) = (x + 2) + 8/(x - 2) or x2 + 4 = (x - 2)(x + 2) + 8
(3x4 + 2x3 - x2 - x - 6)/(x2 + 1)= 3x2 + 2x - 4 + (-3x - 2)/(x2 + 1)= 3x2 + 2x - 4 - (3x + 2)/(x2 + 1)where the quotient is 3x2 + 2x - 4 and the remainder is -(3x + 2).
x4 +x2 =x2 (x2+1)
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
(x2 + 14x + 49) = (x + 7)2
The anti-derivative of X2 plus X is the same as the anti-derivative of X2 plus the anti-derivative of X. The anti derivative of X2 is X3/3 plus an integration constant C1 The anti derivative of X is X2/2 plus an integration constant C2 So the anti-derivative of X2+X is (X3/3)+(X2/2)+C1+C2 The constants can be combined and the fraction can combined by using a common denominator leaving (2X3/6)+(3X2/6)+C X2/6 can be factored out leaving (X2/6)(2X+3)+C Hope that helps
3x4 plus 5x3 plus x2 - 5 divided by x 2 =[(3x4) + (5x3) + (x2 - 5)]/x2 =(12 + 15 + x2 -5)/x2 =(27 - 5 + x2)/x2 =(22 + x2)/x2
2.5
y = 3 + 2x - 4x^(2) dy/dx = 2 - 8x ( The derivative).
Oh honey, you've got yourself a classic case of finding the average of two points in a coordinate plane. All you need to do is add the x-coordinates (x1 + x2) and divide by 2 to get the x-coordinate of the midpoint. Then do the same for the y-coordinates (y1 + y2), divide by 2, and voila, you've got the y-coordinate of the midpoint. Easy peasy lemon squeezy!
Well if you have 5/X then you can rewrite this like 5x-1. And the derivative to that is -5x-2 and that can be rewrote to: -(5/x2).
There are several steps involved in how one can solve the derivative x plus y - 1 equals x2 plus y2. The final answer to this math problem is y'(x) = (1-2 x)/(2 y-1).
The antiderivative of x/(x2-1) is ln(x2-1)/2. Proof: (ln(x2-1)/2)' = (1/(x2-1))*(x2-1)'/2=1/(x2-1)*(2x/2)=x/(x2-1).
2
lim (x3 + x2 + 3x + 3) / (x4 + x3 + 2x + 2)x > -1From the cave of the ancient stone tablets, we cleared away several feet of cobwebs and unearthed"l'Hospital's" rule: If substitution of the limit results in ( 0/0 ), then the limit is equal to the(limit of the derivative of the numerator) divided by (limit of the derivative of the denominator).(3x2 + 2x + 3) / (4x3 + 3x2 + 2) evaluated at (x = -1) is:(3 - 2 + 3) / (-4 + 3 + 2) = 4 / 1 = 1
d/dx (x2+ 9)1/2= 1/2*(x2+ 9)-1/22x = x(x2+ 9)-1/2or x/(x2+ 9)1/2
x3+3x2+3x+2 divided by x+2 equals x2+x+1