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(a) If $f(x, y)=k x y$ is a joint $p d f$ over the region $R$ in Exercise $11,$ determine $k$. (b) Determine $\operatorname{Pr}(E)$ if $E$ is the subset of $R$ defined by $2 \leq x \leq 3$ and $1 \leq y \leq 2$.

(a) $1 / 16$(b) $15 / 64$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 6

Double Integrals

Partial Derivatives

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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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in discussion we have the expression double integral. Are x squared plus y squared minus four. Bu. We are required to find the region in the xy plane. That minimizes its value. So let's see how to solve this question. Let's say this function is JED and Jer will be close to x squared plus y squared minus four. We know that this JED is a parabola Lloyd opening upward with vertex 0:00 -4 hands. We can say that the double integral minimizes if Jack is less than equals to zero. So on the basis of this condition, we can say that the region R will be close to X comma Y X is choir Les vice choir is less than equal to pour. But this is the region R in the xy plane that minimizes the given double integral. So this is the final answer for this problem. I hope you understand the solution. Thank you.

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