Given f(x) = 5x4 – x2 + 6x – 1. What is Limit of f (x) as x approaches negative 1?
2 answers:
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Coordinates of point C: (1,-1)
Step-by-step explanation:
In this problem, A, B and C are collinear, and B is between A and C.
The ratio AB : BC is 3 : 1.
This means that we can write the following two equations:
where:
are the coordinates of point A
are the coordinates of point B
are the coordinates of point C
Solving the equation for ,
Solving the equation for ,
So, the coordinates of point C are
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Answer:
m∠B < m∠A < m∠C
Step-by-step explanation:
We can work with the triangle inequality to find that the side measures form a triangle when n > 5/4. For the given value of n ≥ 4, we don't need to be concerned with whether a triangle is formed or not.
For n = 4, the side lengths are ...
a = 2(4) = 8
b = (4) +3 = 7
c = 3(4) -2 = 10
The longest side is opposite the largest angle, so the ordering of angles is ...
m∠B < m∠A < m∠C
_____
The triangle inequality requires all of these inequalities be true:
- a+b > c ⇒ 3n+3 > 3n-2 . . . always true
- b+c > a ⇒ 4n+1 > 2n ⇒ n > -1/2
- c+a > b ⇒ 5n-2 > n+3 ⇒ n > 5/4
That will be the case for n > 5/4. The attached graph shows the sides and angles keep the same order for n > 3.
