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.
Best Answer: The problem here is not that the limit is undefined, but rather that teh function is multivalued at x = 0. There is a discontinuity at x = 0. There is no asymptote. x/|x| consists of two disconnected lines. That's why the limit at x = 0 does not exist. Just to test it out, work out x/|x| for x = -0.001 and x = +0.001. See what you get. Just as a side note, if you obtained the Fourier series for x/|x|, it would return the value 0 at x = 0.