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You put some ice cubes in a glass, fill the glass with cold water, and then let the glass sit on a table. Describe how the temperature of the water changes as time passes. Then sketch a rough graph of the temperature of the water as a function of the elapsed time.
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The water will cool down almost to freezing as the ice melts. Then, when the ice has melted, the water will slowly warm up to room temperature.
Calculus 1 / AB
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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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Okay. You put some ice cubes in a glass, fill the glass with cold water and then let the glass sit on a table. Describe how the temperature of the water changes as time passes, then sketch a rough draft of the temperature of the water as a function of the lapse time. So maybe it's easiest if I describe the temperature as I'm talking here. Okay, so this glass here is chilling on the table, and it's probably sitting at room temperature and we'll call that, uh, 72 degrees in the house, Okay? And so we fill it with ice cubes and maybe it it drops fairly significantly. Okay. And as we, uh, as we fill the classical water, it's really gonna drop. I don't know how cold it might be. Maybe, uh, you know, 30 degrees, it will drop to okay, maybe 30 degrees there. And so it'll sit at three degrees for a while. And so the I start to know, okay. And so the temperature of the glasses is going to rise, maybe really slowly over time, but eventually it will get back to room temperature. Maybe this happens in a, I don't know, a two hour setting. So here is one hour. There's too hard
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