Limits of a Piecewise Function In Exercises 31 and 32, sketch the graph of f. Then identify the values of c for which lim x → l f ( x ) exists. f ( x ) = { x 2 , x ≤ 2 8 − 2 x , 2 < x < 4 4 , x ≥ 4
Limits of a Piecewise Function In Exercises 31 and 32, sketch the graph of f. Then identify the values of c for which lim x → l f ( x ) exists. f ( x ) = { x 2 , x ≤ 2 8 − 2 x , 2 < x < 4 4 , x ≥ 4
Solution Summary: The author explains that the given function splits into three polynomials, and the limit of the function exists for all values except c = 4. As x approaches 2 from left or right, f (x) approaches 0,
Limits of a Piecewise Function In Exercises 31 and 32, sketch the graph of f. Then identify the values of c for which
lim
x
→
l
f
(
x
)
exists.
f
(
x
)
=
{
x
2
,
x
≤
2
8
−
2
x
,
2
<
x
<
4
4
,
x
≥
4
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
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