Unit 3 HW 1
1. Heat flows normal to isotherms, curves along which the temperature is constant. Find the line
along which heat flows through the point (3, 2) when the isotherm is along the graph of 2x + y
= 22.
d
dx
(2x) +
4x
dx
dx
4x
+ 2y
d
dy
+ 2y
dy
dx

Unit 1 HW 1
r +4
1. Evaluate the function f(r) =
+ 1 at the given values of the independent variable and
simplify.
a) f(-4) =
4+ 4
+1=
0
b) f(96) =
96+ 4
+1=
100
c) f(x 4) =
x4 +4
+1=
+1=0+1=1
x
+ 1 = 10 + 1 = 11
+1
2. Write the equation as given by t

Unit 4 HW1
1. Determine the value of a that makes F(x) an antiderivative of f(x)
f(x) = 24 x
5
, F(x) = a x
6
Go to the website https:/www.symbolab.com/solver/integral-calculator and enter
24 x 5
dx
The answer is 4 x
6
so a = 4
2. Find an antiderivative

Unit 5 HW
1. What is the velocity (in ft/s) of a sandbag 1.75 s after it is released from a hot-air balloon that is
stationary in the air?
V(t) = -32t
V(1.75) = -32(1.75) = -56 ft/s
2. A hoist mechanism raises a crate with an acceleration (in m/s) a =
1+

Unit 2 HW1
1.
Determine the values of x for which the function f(x) =
4
x 49 x
2
2
x 49 x 0
x(x 49) 0 so x 0 and x 49 0 so x 49
Where is the function continuous or not continuous?
The function is not continuous at x = 0 and x = 49
Why is the function cont