Calc. Homework Assignment (PS) 7
Class:
Student Number:
Name:
1. At a certain moment, a moving particle has
velocity v = ⟨2, 2, −1⟩ and a = ⟨0, 4, 3⟩ . Find T,
N, and the decomposition of a into tangential
and normal components.
[§14.5 #25]
3. Refer to the Figure 25 on p.783. f (s, t) denotes the density of seawater at salinity level S
(parts per thousand) and temperature T (degrees Celsius).
a. Calculate the average ROC of density with
respect to temperature from C to A.
b. At a fixed level of salinity, is seawater density
an increasing or decreasing function of temperature?
[§15.1 #46, 48]
2. Find the components aT and aN of the acceleration vector of a particle moving along a
circular path of radius R = 100 cm with constant velocity v0 = 5 cm/s.
[§14.5 #43]
4. Evaluate the limit or determine that the limit
does not exist.
(sin x)(sin y)
xy
(x,y)→(0,0)
lim
[§15.2 #23]
(Over Please)
Calculus Homework Assignment 7
xa y b
=
(x,y)→(0,0) x2 + y 2
0 if a + b > 2 and the limit does not exist if
a + b ≤ 2.
[§15.2 #37]
7. Find the points on the graph of z = 3x2 −4y 2
at which the vector n = ⟨3, 2, 2⟩ is normal to the
tangent plane.
[§15.4 #19]
6. Compute the derivative indicated.
8. Use√the linear approximation to estimate the
value 3.012 + 3.992 . Compare with the value
given by a calculator.
[§15.4 #27]
5. Let a, b ≥ 0. Show that
−y
g(x, y) = xye
[§15.3 #56]
,
lim
gyy (1, 0)