MATH 180 - FALL 2012
PRACTICE PROBLEMS FOR REVIEW SESSION
INSTRUCTOR: FREDERICK T.-H. FONG
Acknowledgement: Problems are extracted or modied from Thomas Calculus (Multivariable) textbook.
(1) Find the outward ux (i.e. normal vector away from the z -axis)
Selected problems 12.4-12.5
When reading someone elses answers, always BEWARE of ERRORS or TYPOS!
(12.4.10) To compute k (i 2j) without cross products:
k (i 2j) = (k i) (k 2j)
= (k i) 2(k j)
Right-hand-rule tells us the vector (k i) points in the directio
Math. 0180
Spring 2011.
Midterm test 1.
Name:
Student #:
Verify that there are 6 problems. Work out the problems on the space provided. If more
space is needed use back side of the pages or scratch paper. No notes, books, or calculators
are allowed.
Pleas
Math. 0180
Spring 2011.
Midterm test 2.
Name:
Student #:
Verify that there are 6 problems. Work out the problems on the space provided. If more
space is needed use back side of the pages or scratch paper. No notes, books, or calculators
are allowed.
Pleas
Quiz 1 Math 180, Spring 2011
Problem 1
Given the parametric equations x = ln t and y = 1 + 2t2 . Find the equation of
the tangent line when t = 1.
Solutions: We need the point and the slope at that point. For the point,
we plug in t = 1, and obtain x = 0,
Quiz 1 Math 180, Spring 2011
Problem 1
Given the parametric equations x = ln t and y = 1 + 2t2 . Find the equation of
the tangent line when t = 1.
Problem 2
Find the length of the curve r = 1/, 2 .
Problem 3
Find the area enclosed in the curve r = 4 + 2 c
Quiz 2 Math 180, Spring 2011
Problem 1
Find a vector function that represents the curve of intersection of x2 + y 2 = 16
and the plane x + z = 5.
Solution: We rst parametrize x and y . Note x2 + y 2 = 16 is a circle
of radius 4. Hence, we can use our usua
Quiz 2 Math 180, Spring 2011
Problem 1
Find a vector function that represents the curve of intersection of x2 + y 2 = 16
and the plane x + z = 5.
Problem 2
Find the equation of the tangent line of the curve r(t) = cos ti + sin tj + k at
t = 0.
Problem 3
F