Capitalism is an economic system based on private ownership of the means of production and their operation for profit. Characteristics central to capitalism include private property, capital accumulation, wage labor, voluntary exchange, a price system, and competitive markets.
f(x) = (x+1)^1/2. Hi Carla, The derivative of $f(x)$ is the limit, as $h$ approaches zero of the difference quotient. \[\frac{f(x + h) - f(x)}{h}.\]. For your function this difference quotient is. \[\frac{(x + h + 1)^{1/2} - (x + 1)^{1/2}}{h}.\]. If you multiply the numerator and denominator by $(x + h + 1)^{1/2} + (x + 1)^{1/2}$ and simplify you will arrive at an expression that can be evaluated as $h$ approaches zero.
The limit of f (x) as x approaches c is L .. Thus for the limit of a function to exist as the independent variable approaches c, the left-hand and right-hand limits must be equal. if and only if. When we say, then, that a function approaches a limit, we mean that Definition 2.2 has been satisfied.gain, when we say that the values of x approach a limit, that limit is never a value of x. There is always a difference between the values of x and their limit. The limit is the boundary beyond which no member of the sequence will pass. We summarize this in the following definition.