PLEASE HELP ME!! Kenji is traveling in Europe and renting a car. He is used to thinking of gasoline amounts in gallons, but in E
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If we simply substitute the value x=2 in the expression we have
which is undefined.
But if we factor both numerator and denominator, we have
Since we are studying the limit as x approaches 2, we can assume that x is not 2. In this case, we can simplify the (x-2) parenthesis, and the expression becomes
And we can evaluate this at 2 with no problems:
So, we have
This means that in this case both left and right limits exist and are the same, so the limit exists, but the function is not defined at x=2. This is a removable discontinuity, because we can define the function as its limit, and we have a continuous function at x=2:
Answer:
- See below
Step-by-step explanation:
<u>Find the intersection of circles</u>
- x² + y² + 2x = 0 and
- x² + y² - 3y = 0
<u>Subtract the equations to find:</u>
- 2x = -3y ⇒ y = -2/3x
<u>By substitution find the points:</u>
- (0, 0) and (-1.385, 0.923)
<u>Find midpoint between these two points:</u>
- x = (0- 1.385)/2 = -0.6925 , y = (0 + 0.923)/2 = 0.4615
<u>Find perpendicular bisector passing through this point:</u>
- y - 0.4615 = 3/2(x + 0.6925)
- y = 1.5x + 0.4615 + 1.5(0.6925)
- y = 1.5x + 1.50025
<u>Find intersection of the lines, it is the center:</u>
- y = 1.5x + 1.50025
- x + 2y + 8 = 0
<u>Solving we get:</u>
- x = -2,75, y = -2.625
<u>Find radius, the distance from center to point (0, 0) and get equation of circle:</u>
- (x + 2.75)² + (y + 2.625)² = (0 + 2.75)² + (0 + 2.625)²
- x² + 5.5x + y² + 5.25y = 0
- 4x² + 22x + y² + 21y = 0
- 4x² + 4y² + 22x + 21y = 0
