SOLVED: If H is the Heaviside function defined in Example 6 in Section 2.2, prove, using Definition 2, that lim t →0 H(t) does not exist. [Hint: Use an indirect proof as follows. Suppose that the limit is L . Take ε=(1)/(2) in the definition of a limit and try to arrive at a contradiction. ] | Numerade

Valve Type Primary Function Common Applications in Petroleum Industry Gate Valve On/Off Isolation Used where straight-line flow and minimum restriction are needed. Common in wellheads, pipelines, and tank farms. Not for flow regulation. Ball Valve Quick On/Off Isolation Excellent shut-off capability. Used in offshore platforms, pipeline scraper traps (launchers/receivers), and fuel handling systems. Fire-safe designs are critical. Globe Valve Flow Regulation / Throttling Precisely controls flow

SOLVED: The Heaviside function is used in engineering applications to model flipping a switch. It is defined below:0 if x 0 Sketch the graph of H on the interval [-1, 1]: Does lim H(x) exist? x -> 0 Choose the correct graph below:0AH(x)Does lim H(x) exist? x -> 0 No, because the function has an open circle at (0, 0). Yes, because the function is defined for every value of x in the range [1, 1]. No, because the value of lim H(x) = 0 0 - H(0) = 0. Yes, because the value of lim H(x) = 1.5 is equal