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.
If we do that, then f (x) will be continuous at x = 2 -- because the limit at that value will be the value of the function. (Definition 3 .). When we are able to do that -- define a function at a value where it is undefined and therefore discontinuous -- we say that the function has a removable discontinuity. (x) therefore is continuous at x = 8. (Definition 3 .). In this same way, we could show that the function is continuous at all values of x except x = 2. This is an example of a perverse function, in which the function is deliberately assigned a value different from the limit as x approaches 1.