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In this section we discussed examples of ordinary, everyday functions: Population is a function of time, postage cost is a function of weight, water temperature is a function of time. Give three other examples of functions from everyday life that are described verbally. What can you say about the domain and range of each of your functions? If possible, sketch a rough graph of each function.
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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.
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Hi, My name is Jeffrey and we'LL be doing a problem from section one point one, number six from Stuart's expeditions. In this section, we discuss examples of ordinary everyday functions. Population is function of time. Postage cost is a function of way water temperatures of all time Give three examples of functions from everyday life that are described verbally and what you see about their domain and range and sketched a rough draft if possible. Okay, so I had to cook up three examples on my own, and one of them is gonna include emptying a bathtub. So for a number one here, emptying a bathtub is going to be a function of heights over time. It so height of the water as a function, Uh, time. Okay. So in our graph here, it looks like maybe if the heights, we're to start at twenty four inches off the ground, OK? And the water is going to drain at a constant rate until the height of the water is zero. Maybe it takes five minutes for that's happened. You mean takes five minutes. What happened? So it looks like we're gonna have ahh linear graph here and the domain of this function will hate this height function is gonna be the set of all acts such that ex belongs from time zero Teo five minutes and the range of the height function here. Correspondence tio the vertical axis, the height they will call it. Why I said, Well, why such that? Why belongs from zero inches off the ground? Teo twenty four inches off. And so, for our second example, I thought of the temperature of and the temperature of the oven when baking cookies. So, Theo, we're talking about temperature. That's a function temperature as a function of time. Okay, so I think home, you know, it's usually around indoors at the home is usually around No. Seventy four degrees, I'll say his seventy degrees as it's pre pre heating. Uh, maybe at a constant rate. Here is the supreme heat up tio three hundred fifty degrees and maybe it takes, I don't know, ten minutes for that there, and we're baking cookies for I don't know. Let's see twenty minutes so it stays at the temperature of the oven, stays at three hundred fifty degrees for twenty minutes, and then it needs to cool down all the way back to temperature, which is at seventy four threes. And maybe it takes just this much time. So maybe this is it. Minutes there, maybe two, three minute or to cool down. So let's talk about the domain of this temperature function, okay? And that's going to be the set of all acts. Such that ex belongs from zero Teo, uh, minutes for the range Respons Teo, the temperature of the oven. Hey. And so I guess the temperature of the heaven belongs from seventy four degrees all the way. Teo three hundred. And for this last one here, I said, um, writing a bike down the street. Okay. Riding a bike down the street. So this is a function a speed over time. Its speed is a function. Uh, hi, Purses. So when I ride my bike, I need t o start at, uh, you know, my philosophy starts at zero. Obviously and accelerate a little bit. So maybe it takes Maybe I take off like this here, and I reach a top speed of twenty miles per hour and maybe I I stay at twenty miles per hour and maybe I could get a little bit faster than that. But then, at the end of the street, I need Teo. Stop at the stop sign. So there you are there. So the domain of dysfunction will call it the domain of speech function. Here s is this edible acts he reckons any time such that Immediate. Oh, so maybe this takes no three minutes or all of this event happened. So explosions from zero to three minutes as I ride my bike down the street and the range corresponds to how fast I'm going, the speed you is the center of all. Why such that? Why along from zero miles per hour Tio watching.
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