For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form A x + B y = C with fractional coefficients. (See Example 3-4) Passes through 3 , − 1 and is parallel to the line defined by − 3 x + y = 4.
For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form A x + B y = C with fractional coefficients. (See Example 3-4) Passes through 3 , − 1 and is parallel to the line defined by − 3 x + y = 4.
Solution Summary: The author explains the slope intercept form of a line passing through (3,-1) and parallel to 3x+y=4.
For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form
A
x
+
B
y
=
C
with fractional coefficients. (See Example 3-4)
Passes through
3
,
−
1
and is parallel to the line defined by
−
3
x
+
y
=
4.
Topic 2
Evaluate S
x
dx, using u-substitution. Then find the integral using
1-x2
trigonometric substitution. Discuss the results!
Topic 3
Explain what an elementary anti-derivative is. Then consider the following
ex
integrals: fed dx
x
1
Sdx
In x
Joseph Liouville proved that the first integral does not have an elementary anti-
derivative Use this fact to prove that the second integral does not have an
elementary anti-derivative. (hint: use an appropriate u-substitution!)
1. Given the vector field F(x, y, z) = -xi, verify the relation
1
V.F(0,0,0) = lim
0+ volume inside Se
ff F• Nds
SE
where SE is the surface enclosing a cube centred at the origin and having edges of length 2€. Then,
determine if the origin is sink or source.
4
3
2
-5 4-3 -2 -1
1 2 3 4 5
12
23
-4
The function graphed above is:
Increasing on the interval(s)
Decreasing on the interval(s)
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