<span>1. We analyze the limit by approaching it from both the left and the right.
From the left: f(x) = x + 10 (for x < 8), as x --> 8, f(x) --> 18
From the right: f(x) = 10 - x (for x >= 8), as x --> 8, f(x) --> 2
Since the limits on either side do not converge to the same point, the limit does not exist (this is choice C).
2. </span>Using a similar approaching as in #1:
<span><span>From the left: f(x) = 5 - x (for x < 5), as x --> 5, f(x) --> 0
At x = 5 itself: f(x) = 8
From the right: f(x) = x + 3 (for x > 5), as x --> 5, f(x) --> 8</span>
Although the value at x = 5 matches with the limit when approaching from the right, the limit when approaching from the left doesn't match, so the limit does not exist (choice D).
3. </span><span><span>From the left: f(x) = 5x - 9 (for x < 0), as x --> 0, f(x) --> -9
From the right: f(x) = |2 - x| (for x >= 0), as x --> 0, f(x) --> 2
</span>Again, since the limits when approaching from the left and right don't match, the limit does not exist. (This is Choice D).
4. lim 1/(x - 4) as x -->4-
If we are approaching x = 4 from the left, we can test values such as 3, 3.9, 3.99, 3.999, approaching 4. For x = 3, f(x) = -1. For x = 3.9, f(x) = -10. For x = 3.99, f(x) = -100. For x = 3.999, f(x) = -1000. This shows that the value continues to go towards negative infinity.
If we were to graph these 4 points on the Cartesian plane, it would also show a curve to slopes downwards to negative infinity, with the vertical asymptote at x = 4. The correct answer is Choice C) -∞ ; x = 4.
5. </span>f(x) = (x+1)(x-1) / [(x+1)(x-2)] is an example of a function with both a removable and non-removable discontinuity.
In this case, because x+1 cancels out from the numerator and denominator, it results in a hollow or missing point (removable) discontinuity at x = -1. This means that the limit still exists as x --> -1. On the other hand, x = 2 is a non-removable discontinuity, since it cannot be cancelled out, and it will be an asymptote.
Answer:
51 trees
Step-by-step explanation:
Start at one end of the 50-foot line segment.
At position 0 ft, put one tree.
Then 1 ft from 0 ft, put tree number 2.
One more foot over, at position 2 ft from the start, put tree number 3.
Notice that each tree number is one more than the number of feet.
That means at 50 ft from the stat, you put tree number 51.
Answer: 51 trees
Answer:
They scored 66 points
Step-by-step explanation:
Sally scored 45% out of the 100%
And there are 120 points in all.
To find the rest of the teams points you have to subtract Sally's points:
100% - 45% = 55
So to find this out you solve for x (points):
55/100 = x/120
100x = 6,600
100x = 6,600
100 100
x = 66
Step-by-step explanation:
