Minimize f(x, y, z) = xy + xz+yz subject to x² + y² + z² = If R = [0, ] ×[1, 2], compute fr sin(xy) dA. Т 2 -2
Minimize f(x, y, z) = xy + xz+yz subject to x² + y² + z² = If R = [0, ] ×[1, 2], compute fr sin(xy) dA. Т 2 -2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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#3 please.
![### Calculus Problems
3. **Minimize**
Minimize \( f(x, y, z) = xy + xz + yz \) subject to \( x^2 + y^2 + z^2 = 2 \) and \( z = 1 \).
4. **Double Integral Calculation**
If \( R = [0, \pi] \times [1, 2] \), compute
\[
\iint_R x \sin(xy) \, dA.
\]
5. **Evaluate the Double Integral**
Evaluate
\[
\int_0^2 \int_0^2 \sin(x^2/2) \, dx \, dy.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dc3ef7d-848e-4463-9030-e4a43ebc2b5f%2F8098a4bd-1864-44a3-8a24-ca494491ec89%2Fgh1f5o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Problems
3. **Minimize**
Minimize \( f(x, y, z) = xy + xz + yz \) subject to \( x^2 + y^2 + z^2 = 2 \) and \( z = 1 \).
4. **Double Integral Calculation**
If \( R = [0, \pi] \times [1, 2] \), compute
\[
\iint_R x \sin(xy) \, dA.
\]
5. **Evaluate the Double Integral**
Evaluate
\[
\int_0^2 \int_0^2 \sin(x^2/2) \, dx \, dy.
\]
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