MATH 177
Problem Set # 6
Note : Problems marked with are left for students to do at home.
1. Given that the relation 2x 3 y 2 + yz 4 xz = 2 implicitly defines x as a differentiable function
of y and z ; that is x = xy, z. Find x .
z
2. The relation x 5 +
MATH 177
Problem Set # 2
Note : Problems marked with are left for students to do at home.
1. In each case identify the plane curve given by the specified vector equation :
i r t = 2 + t i + 4 + 8t j ,
0 t 1.
ii r t = 2 + 6 cost i + 4 + 8 sint j ,
0 t 2.
i
MATH 177
Problem Set # 1
Note : Problems marked with are left for students to do at home.
1. The position vector of a particle at time t is given by r t = t 2 2t i + 6t 10 j + 2 t 3/2 k .
Find the velocity , acceleration , and the speed of the particle at
MATH 177
Problem Set # 4
Note : Problems marked with are left for students to do at home.
1. Let z = x 4 + 2xy , where x = 1 sin2t , and y = t ln1 + t.
Use the Chain Rule to find dz at t = 0.
dt
2. Let W = x 2 + 2xyz , where xt = e t , yt = tan3t + 1 , an
MATH 177
Problem Set # 3
Note : Problems marked with are left for students to do at home.
1. In each case , find the Domain of f and Sketch :
a
fx, y =
1
x2 y
c
fx, y =
7
b
x2 + y2 1
d
fx, y = ln2x y
fx, y =
ln2x y
2. Draw a Contour Map with Four Level Cu
MATH 177
Problem Set # 5
Note : Problems marked with are left for students to do at home.
1. Find an equation of the plane tangent to the surface z =
5
x 3 + y 2 at the point on surface
where x = 2 , and y = 3.
2. Find the coordinates of all points on the
MATH 177
Problem Set # 7
Note : Problems marked with are left for students to do at home.
1. In each case find the x and y coordinates of the critical points of the given function f x, y :
i
f x, y = x 4 4xy + 2y 2 + 9.
3
2
ii f x, y = e xy 3x +24y1
iii f