The document contains various questions on the topics of calculus 2. The questions are brief and understandable and should be solved in under 2 hours. Some questions may require you to spend some more time than the other but all and all, read every question thoroughly and this paper may help you a ...
HABIB UNIVERSITY
Math 102 Test 2
Spring Semester 2019
INSTRUCTIONS:
Please show all your work wherever possible and attempt all questions. You may use a calculator, but do show
the work and explain your thinking wherever possible / applicable. For MCQs, circle only ONE answer. You
have 60 minutes. Good luck!
1. A plane is drawn through the points P = (2, 1, 0), Q = (0, 1, 3) and R = (1, 0, 1).
(a) Which of the following is a normal vector to the plane? [2]
! ! ! ! ! ! ! ! ! ! ! !
A. ! 3i + j + 2k B. ! 3i − j + 2k C. ! 2i − j + 3k D. ! −3i − j − 2k
(b) Which of the following is the equation of the plane containing P, Q, and R? [2]
5 − 3x + y
A. ! 3x + y + 2z = 5 B. ! z = C. ! 2x − y + 3z = 5
2
2. The contour plot of a function f is given.
(a) Use the contour plot to determine the signs
(negative or positive) of! f x (2,1) and f y (2,1). [2]
f x (2,1) is ___________
f y (2,1) is ___________
(b) Use the plot to estimate the value of ! f y (2,1) . [2]
(c) Mark an X on the contour for where you think there is a local minimum on the function f. [1]
, 3. Given a particular function, f (x, y), which of the following is the expression for the derivative at f (2, 1)
! !
in the direction of vector! i − j ? [2]
f y (2,1)
( f (2,1)) ( f (2,1)) f x (2,1)
2 2
A. ! f x (2,1) − f y (2,1) B. ! x
+ y
C. ! −
2 2
4. Which of the following is the normal vector to the curve ! x 2 − y 2 = 3 at the point (2, 1)? [2]
! ! ! ! ! ! ! !
A. ! i − j B. ! 4i − j C. ! 4i + 2 j D. ! 4i − 2 j
1
5. Find an equation of the tangent plane to the surface ! z − = 0 at the point (1, 1, 1). [4]
xy
The benefits of buying summaries with Stuvia:
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
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
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 radhikakhatri. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.49. You're not tied to anything after your purchase.
