A Movie theater sold 5 times as many children's tickets as adult tickets to an afternoon show. If 132 tickets were sold in all,
how many were children's tickets?
1 answer:
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I believe the given limit is
Let
Now rewrite the expression as a difference of cubes:
Then
The limit is then equivalent to
From each remaining cube root expression, remove the cubic terms:
Now that we see each term in the denominator has a factor of <em>x</em> ², we can eliminate it :
As <em>x</em> goes to infinity, each of the 1/<em>x</em> ⁿ terms converge to 0, leaving us with the overall limit,
Answer:
x=-2.5 if the function is
Step-by-step explanation:
has discontinuities when the denominator is 0.
You will either have a hole or a vertical asymptote depending on what happens to the numerator after you find when the bottom is 0.
That is whatever you found that makes the bottom 0, if it makes the top also 0 then you will have a hole at x=the number that made the bottom 0.
If it makes the top anything other than 0, then it is a vertical asymptote at x=the number you found that made the bottom 0.
Let's do this now.
When is -4x-10 equal to 0?
We have to solve the equation:
-4x-10=0
Add 10 on both sides:
-4x=10
Divide both sides by -4:
x=10/-4
Reduce by dividing top and bottom by 2:
x=5/-2
x=-5/2
or
x=-2.5 (if you want decimal form)
Now does it make the top 0? This is the deciding factor on whether you have a hole at x=-2.5 or a vertical asymptote at x=-2.5.
Let's see.
8(-2.5)-3=-23
Since the top is not 0 at x=-2.5 then you have a vertical asymptote at x=-2.5.
If the top were 0, then you would have had a hole at x=-2.5.