Answer:
Anything in the form x = pi+k*pi, for any integer k
These are not removable discontinuities.
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Explanation:
Recall that tan(x) = sin(x)/cos(x).
The discontinuities occur whenever cos(x) is equal to zero.
Solving cos(x) = 0 will yield the locations when we have discontinuities.
This all applies to tan(x), but we want to work with tan(x/2) instead.
Simply replace x with x/2 and solve for x like so
cos(x/2) = 0
x/2 = arccos(0)
x/2 = (pi/2) + 2pi*k or x/2 = (-pi/2) + 2pi*k
x = pi + 4pi*k or x = -pi + 4pi*k
Where k is any integer.
If we make a table of some example k values, then we'll find that we could get the following outputs:
- x = -3pi
- x = -pi
- x = pi
- x = 3pi
- x = 5pi
and so on. These are the odd multiples of pi.
So we can effectively condense those x equations into the single equation x = pi+k*pi
That equation is the same as x = (k+1)pi
The graph is below. It shows we have jump discontinuities. These are <u>not</u> removable discontinuities (since we're not removing a single point).
Well 43 ones times 3 tens is basically 43 times 30 which is 1,290
then divide that by ten to get how many tens and you will get 129 tens
hope this helps
49 divided by 3 = 16.33
Each sibling has about 16 rare coins.
Answer:
A. E={
and
is a multiple of 8}
Step-by-step explanation:
Let
represent the set of natural numbers. Then we can write;
.
The set of all natural numbers that are multiples of 8 is then written as;
and
is a multiple of 8.
E is the set of natural numbers that are multiples of 8 can then be written in set builder notation as;
E={
and
is a multiple of 8}
The correct choice is A