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The Heaviside function defined in Exercise 59 can also be used to define the ramp function $ y = ctH(t) $ , which represents a gradual 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 gradually increased to 120 volts over a 60-second time interval. Write a formula for $ V(t) $ in terms of $ H(t) $ for $ t \le 60 $.(c) Sketch the graph of the voltage $ V(t) $ in a circuit if the switch is turned on at time $ t = 7 $ seconds and the voltage is gradually increased to 100 volts over a period of 25 seconds. Write a formula for $ V(t) $ in terms of $ H(t) $ for $ t \le 32 $.
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Calculus 1 / AB
Calculus 2 / BC
Functions and Models
New Functions from Old Functions
Functions of Several Variables
January 2, 2022
Nevermind. Got it 120 vols over 60 sec = slope of 2
Looks like I am missing something basic. Both authors say c = 2t. Where is that 2 coming from? Could someone explain.
August 16, 2020
Part c), when t=7, V(7)=0, so the slope of the graph should be from 0 to 100 for [7,32]
Harvey Mudd College
University of Nottingham
Idaho State University
A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.
In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.
The Heaviside function def…
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So for the given problem um we can use it to define the ramp function Y equals C. T. Hft. Um Which is going to represent a gradual increase in the voltage or current in a circuit. So we're going to sketch the graph of the ramp function. We see the voltage is going to be in this case C is going to be too so we'll have to t 3 50. And then given the ramp function we'll eventually end up getting um Since this is Changing turned on at seven seconds we'll have four Times T -7 yeah. of eight times at age 15 and seven. So that will be our final uh resulting function for the voltage.
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