I need help!!!!!!!!!!!!!!!!!
1 answer:
Answer:
1. 4 2. 2 3. Does not exist 4. Does not exist 5. 3
Step-by-step explanation:
1. This is the limit as x approaches 2 <u>from the left</u>. That means that x "sneaks up" on 2, but <u>from</u> the left (ironically moving right). As x does that, the graph rises, heading for 4 (even though the point is "empty"). The limit is 4. See attached image 1
2. Let x sneak up on 2 <u>from the right</u> (so moving left towards 2). As x does that, the graph falls, heading for the y-value 2. The limit is 2. See image 2.
3. This limit (two-sided) does not exist because the one-sided limits had <u>different</u> values.
4. This limit does not exist, either. The limit as x approaches 0 from the left is 4. The limit as x approaches 0 from the right is 0. These are different, so the two-sided limit is not defined.
5. g(2) = 3, where the solid dot is. It's the value of the function <u>at</u> x=2.
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Answer:
<em>Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295, so I will take the car to Amy's shop</em>
<em>Point of intersection: (x,y) = (4,360)</em>
Explanation:
Part 1 )
Let x = number of hours worked
Let y = total cost to you
Determining where to take the car:
<em>Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295</em>
Mike's repair shop:
Service fee: $100
Per hour rate: $65
Let x is the number of hours worked on. Total cost will be equal to the service fee plus hourly charges. Charges per an hour are $65, so for x hours the charges will be 65x.
Therefore, total cost for Amy's repair shop can be written as:
y = 100 + 65x ------(1)
For 3 hours work: y = 100 + 65(3)
<em>Cost at Mike's, y = $100 + $195 = $295</em>
<em>Amy's repair shop: </em>
Service fee: $40
Per hour rate: $80
Charges per an hour are $40, so for x hours the charges will be 80x.
Therefore, total cost for Amy's repair shop can be written as:
y = 40 + 80x ------(2)
For 3 hours work: x = 3
y = 40 + 80(3)
<em>Cost at Amy's, y = $40 + $240 = $280</em>
<em>Part 2)</em>
<em>Find the point of intersection</em>
<em>Using elimination method:</em>
<em>y = 100 + 65 x ------1</em>
<em>y = 40 + 80x ------2</em>
<em>As the y coefficients are equal we will subtract eq1 from eq2</em>
<em>y - y = 40 + 80x - 100 - 65x</em>
<em>0 = -60 + 15x</em>
60 = 15x
x =
x = 4
put x = 4 in eq 1
we get y = 100 + 65 (4) = 100 + 260 = 360
x = 4, y = 360
Point of intersection: (x,y) = (4,360)