What is the equation of a line with a slope of −4−4 and a point (−2,5)(−2,5) on the line? Express the equation in th
2 answers:
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The first limit is known as a left-hand limit. We're approaching x = 3 from the left. This means we start with values smaller than x = 3, say x = 2.5 and move closer to x = 3.
Because x is starting off smaller than 3, we use the first piece of the piecewise function. This is the piece that corresponds to x < 3. So we plug x = 3 into that piece to get
2x^2 - x = 2(3)^2 - 3 = 2(9) - 3 = 18 - 3 = 15
So the result for the left-hand limit is 15.
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The right hand limit will have us start on the other side of x = 3. We start at x = 3.5 and move closer to x = 3. So we'll use the
portion.
Plug x = 3 into the second piece to get
3 - x = 3 - 3 = 0
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The result of the left-hand limit was 15
The result of the right-hand limit was 0
The fact that the results do not match up means that the overall limit at x = 3 does NOT exist.
Because x is starting off smaller than 3, we use the first piece of the piecewise function. This is the piece that corresponds to x < 3. So we plug x = 3 into that piece to get
2x^2 - x = 2(3)^2 - 3 = 2(9) - 3 = 18 - 3 = 15
So the result for the left-hand limit is 15.
----------------------------------------------------------
The right hand limit will have us start on the other side of x = 3. We start at x = 3.5 and move closer to x = 3. So we'll use the
Plug x = 3 into the second piece to get
3 - x = 3 - 3 = 0
--------------------------------------------------------------------------
The result of the left-hand limit was 15
The result of the right-hand limit was 0
The fact that the results do not match up means that the overall limit at x = 3 does NOT exist.
To complete the table it is necessary to know the possibilities that the sergeant has to change or remain in an intersection. The probabilities (depending on the box) are:
- 0
- 0.2
- 0.25
- 0.33
<h3>How to calculate the probability of intersection change? </h3>
To know the probability of intersection change, it is necessary to locate the police officer at one of the intersections. Subsequently, count how many possibilities of change you have, for example: 3 possibilities and finally add the possibility of remaining in the intersection as shown below:
- Intersection 3 has 3 possibilities of changing towards intersections 2, 8 and 4. Additionally, it has the possibility of staying at intersection 3, that is, it has 4 possible decisions.
To know the probability we divide the number 1 (because it is only a decision that we have to make) and divide it by the number of possibilities (4).
- 1 ÷ 4 = 0.25
According to the image we can infer that in some intersections they only have 3, 4 and 5 possibilities, so the probability of change will be different as shown below:
- 1 ÷ 3 = 0.33
- 1 ÷ 4 = 0.25
- 1 ÷ 5 = 0.2
Learn more about probabilities in: brainly.com/question/8069952
