The magnitude of the vector to two decimal places is 11.40 units
The formula for calculating the magnitude of the vector is expressed as:
Given the coordinate points (-3, 4) and (6, -3)
Hence the magnitude of the vector to two decimal places is 11.40 units
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20. A rational function (where
are polynomials in
) has a removable discontinuity at
if for some positive integer
we can factorize
That is, we "remove" the discontinuity at because while
, we have
. The discontinuity is still there, since
is undefined, but in the limit sense we can essentially ignore the factors of
. The graph of
will have all the features of
aside from a hole at
.
In this case, we have
and when , we can cancel the factor of
so that
("DNE" = "does not exist", i.e. is undefined. For some reason "undefined" wouldn't render...)
This means is a removable discontinuity.
We cannot do the same with the factor of , so in contrast
is a non-removable discontinuity.
21. The pieces of defined on
and
are themselves continuous since they are polynomials. Then the continuity of
over the entire real line depends on the point where the pieces meet.
Here we have
so the pieces meet at . Continuity at this point requires that the both limits from either side of
be the same. This means
Solve for .