Challenge Problem Removing a Discontinuity In Example 5 we graphed the rational function R ( x ) = 2 x 2 − 5 x + 2 x 2 − 4 and found that the graph has a hole at the point ( 2 , 3 4 ) . Therefore, the graph of R is discontinuous at ( 2 , 3 4 ) . We can remove this discontinuity by defining the rational function R using the following piecewise-defined function: R ( x ) = { 2 x 2 − 5 x + 2 x 2 − 4 if x ≠ 2 3 4 if x = 2 Redefine R from Problem 33 so that the discontinuity at x = 3 is removed. Redefine R from Problem 33 so that the discontinuity at x = 3 2 is removed. R ( x ) = x 2 + x − 12 x 2 − x − 6
Challenge Problem Removing a Discontinuity In Example 5 we graphed the rational function R ( x ) = 2 x 2 − 5 x + 2 x 2 − 4 and found that the graph has a hole at the point ( 2 , 3 4 ) . Therefore, the graph of R is discontinuous at ( 2 , 3 4 ) . We can remove this discontinuity by defining the rational function R using the following piecewise-defined function: R ( x ) = { 2 x 2 − 5 x + 2 x 2 − 4 if x ≠ 2 3 4 if x = 2 Redefine R from Problem 33 so that the discontinuity at x = 3 is removed. Redefine R from Problem 33 so that the discontinuity at x = 3 2 is removed. R ( x ) = x 2 + x − 12 x 2 − x − 6
Challenge Problem Removing a Discontinuity In Example
5
we graphed the rational function
R
(
x
)
=
2
x
2
−
5
x
+
2
x
2
−
4
and found that the graph has a hole at the point
(
2
,
3
4
)
. Therefore, the graph of
R
is discontinuous at
(
2
,
3
4
)
. We can remove this discontinuity by defining the rational function
R
using the following piecewise-defined function:
R
(
x
)
=
{
2
x
2
−
5
x
+
2
x
2
−
4
if
x
≠
2
3
4
if
x
=
2
Redefine
R
from Problem
33
so that the discontinuity at
x
=
3
is removed.
Redefine
R
from Problem
33
so that the discontinuity at
x
=
3
2
is removed.
Calculus lll
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3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i,
and i.
(a) Verify the relations between this roots and the coefficients of the polynomial.
(b) Find the annulus region in which the roots lie.
Force with 800 N and 400 N are acting on a machine part at 30° and 60°, respectively with the positive x axis
Chapter 4 Solutions
Mylab Math With Pearson Etext -- Standalone Access Card -- For Precalculus (11th Edition)
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