SOLVED:If H is the Heaviside function defined in Example 6, prove, using Definition 4, that limt →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.]
SOLVED:If H is the Heaviside function defined in Example 6, prove, using De…
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The Heaviside function defined in Exercise 57 can also be usedto define the ramp function y=c t H(t), which represents agradual increase in voltage or current in a circuit.(a) Sketch the graph of the ramp function y =tH(t) . (b) Sketch the graph of the voltage V(t) in a circuit if the switch is turned on at time t =0 and the voltage is graduallyincreased to 120 volts over a 60 -second time interval. Writea formula for V(t) in terms of H(t) for t ⩽ 60.(c) Sketch the graph of the volta
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