Answer:
The equation of the required line in the slope-intercept form is
y = -3x + 10
Step-by-step explanation:
i) the required line passes through the point (5, -5)
ii) the required line is also parallel to the line 3x + y = -2 ⇒ y = -3x - 2
Therefore the slope of the given line is -3.
Therefore the slope of the required line is also -3
The equation of the required line in the slope-intercept form is
y - (-5) = -3(x - 5) ⇒ y + 5 = -3x + 15 ⇒ y = -3x + 10 ∴ 3x + y = 10.
Answers:
The limit as x approaches 3 does not exist (DNE)
The function value f(3) is equal to 5, so f(3) = 5
In short, the answer is choice B
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Explanations:
Let's start with computing the limit. First locate 3 on the x axis. Then move slightly to the left of 3, say to x = 2. Draw a vertical line upward until you hit the function curve. Mark the point on the function curve and then drag that point closer and closer to x = 3. Notice how y is getting loser to y = 3.
Then do the same for the other side of x = 3. Start at x = 4 and move to the left to get to x = 3. Get closer and closer, and you'll notice that y is getting closer to y = 5. These two differing y values tell us that the limit as x approaches 3 does not exist.
Alternatively: The left hand limit (LHL) and right hand limit (RHL) are different, so the overall limit does not exist.
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The function value f(3) is simply 5 because we draw a vertical line through x = 3 and it intersects the function at (3,5). Take note how I'm focusing on the closed circle and not the open circle. The open circle is a gap or hole in the graph.
Note: because the limit at x = 3 and the function value at x = 3 differ, this means we have a discontinuity.
(5x) / (2/11) = 3 / (1/5)
cross multiply
(5x)(1/5) = (2/11)(3)
x = 6/11
