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Trees grow faster and form wider rings in warm years and grow more slowly and form narrower rings in cooler years. The figure shows ring widths of a Siberian pine from 1500 to 2000.

(a) What is the range of the ring width function?(b) What does the graph tend to say about the temperature of the earth? Does the graph reflect the volcanic eruptions of the mid-19th century?

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a) $Re [0,1.5]$b) see explanation

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 1

Four Ways to Represent a Function

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

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University of Michigan - Ann Arbor

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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.

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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. Number twelve here trees grow faster and form waterings and warn ears and grow more slowly. Inform narrower, narrower brains and cooler years. Figure shows rings with a severe in pine from fifteen hundred to two thousand. And so, for this first part, what is the range of the ring with function? Okay, so in other words, where does t range? Okay. And Oh, not tea. But this or actually what is our range? Ours in range from zero all the way up, Tio. Maybe one point five. I don't guess here. So for a R range is from zero Tio, we said one point side there. Okay. And what does the graph tend to say about the temperature of the earth? Well, if you re here, trees grow faster and former white earrings and warm years and slowly and narrow number and pool years if you notice the temperature. You know, on average days about the same. Although, live Teoh right before nineteen hundred. Okay, but as you can see, there isn't a rise. Okay? And the ring with here, you can see that there is a linear approximation to the ring with hey, and it's increasing. So maybe the temperature from right before nineteen hundred to two thousand. And even now it's Ah, it's getting warmer

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