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a limit is concerned with how a funciton behaves very close to a certain point.

it is written simply as limf(x) = A, x>a

this means as x approaches a, f(x) equals A

As we are told the number of girls that are in the school, our first step should be to calculate the number of boys in the school through a simple subtraction (1200-575 = 625). After this we are told that...

X+2/5X = 63 or 63 = 140%

First we need to understand that the original price (X) has been increased by 40%. Hence, by 2/5 (40/100 = 40%) of its original value, in other words, 2/5X.

To find ...

Notice that the square root of 8 can be simplified: 4 / (sqrt(4) * sqrt(2) + 4) = 4 / (2 * sqrt(2) + 4) Divide top and bottom of the fraction by two: 2 / (sqrt(2) + 2) Rationalise the denominator: (2 / (s...

So this function is the product of two functions of x, so we use the product rule to differentiate it. The rule states if y=uv, dy/dx=(du/dx)v+(dv/dx)u. In this function we assign u=(4x+1)³ and...