100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
WGU C656 - MATH 3311 Calculus III - Complete FA Review 2024. $12.49   Add to cart
Quickly navigate to
Preview
  2.  
  3. Western Governers University
  4.  
  5. Education

Exam (elaborations)

WGU C656 - MATH 3311 Calculus III - Complete FA Review 2024.
 8 views  0 purchase

WGU C656 - MATH 3311 Calculus III - Complete FA Review 2024.WGU C656 - MATH 3311 Calculus III - Complete FA Review 2024.WGU C656 - MATH 3311 Calculus III - Complete FA Review 2024.WGU C656 - MATH 3311 Calculus III - Complete FA Review 2024.

Preview 3 out of 29  pages

Document information

  • August 19, 2024
  • 29
  • 2024/2025
  • Exam (elaborations)
  • Unknown

Subjects

  • wgu c656 math 3311 calculus iii complete fa re

Written for

All documents for this subject (58)

Seller

avatar-seller
Bankart

Reviews received

Content preview

C656 MATH 3311




Calculus III




COMPLETE FA REVIEW




© 2024

,1. Question:
What condition must a vector field F satisfy to be conservative?
a) \( \nabla \cdot \mathbf{F} = 0 \)
b) \( \nabla \times \mathbf{F} = 0 \)
c) \( \nabla \mathbf{F} = 0 \)
d) \( \int_{C} \mathbf{F} \cdot d\mathbf{r} = 0 \)


Answer: b) \( \nabla \times \mathbf{F} = 0 \)


Rationale: A vector field is conservative if and only if its curl is
zero.


2. Question:
Evaluate the integral \( \int_{0}^{1} \int_{0}^{x} xy \, dy \, dx \).
a) \( \frac{1}{8} \)
b) \( \frac{1}{4} \)
c) \( \frac{1}{6} \)
d) \( \frac{1}{2} \)

© 2024

, Answer: b) \( \frac{1}{4} \)


Rationale: First, integrate with respect to \(y\), giving \(
\int_{0}^{1} \left[ \frac{1}{2}xy^2 \right]_0^x dx \), resulting in \(
\frac{1}{2} \int_{0}^{1} x^3 \, dx = \frac{1}{4} \).


3. Question:
Which of the following integrals represents the surface area of
the paraboloid \( z = 4 - x^2 - y^2 \) for \( z \geq 0 \)?
a) \( \iint_{D} 1 \, dA \)
b) \( \iint_{D} \sqrt{1 + (\nabla z)^2} \, dA \)
c) \( \iint_{D} \sqrt{1 + (2x)^2 + (2y)^2} \, dA \)
d) \( \iint_{D} \sqrt{16 - x^2 - y^2} \, dA \)


Answer: c) \( \iint_{D} \sqrt{1 + (2x)^2 + (2y)^2} \, dA \)


Rationale: The surface area integral formula over a region \(D\)
requires the integrand \( \sqrt{1 + (\frac{\partial z}{\partial x})^2 +
(\frac{\partial z}{\partial y})^2} \).


4. Question:
© 2024

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller Bankart. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $12.49. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

83662 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$12.49
  • (0)
  Add to cart