<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.
The cactus one I think is 0.875
Answer:
$45 more
(but honestly I think I would spend longer mowing their lawns to try and make some more profit)
Step-by-step explanation:
Mr. Smith requires 4 1/2 hours.
Mrs Jones requires 7 1/2 hours.
7 - 4 = 3
3 * 15 = $45
A line <u>bisector</u> is a <em>straight </em>line that <u>divides</u> a given line into two equal parts. Thus the following steps are required by Naomi to show that point D is <em>equidistant</em> from points A and C.
BD ⊥ AC (given)
BD = 3 units, and AC = 8 units.
BD is the <em>perpendicular</em> bisector of <u>segment</u> AC (given)
Thus,
<BDA ≅ <BDC <em>(right</em> angles formed by a <u>perpendicular</u> bisector)
AD ≅ DC <em>(equal</em> parts of a<em> bisected l</em>ine)
AD ≅ DC = 4 units
Thus joining <u>points</u> B to A, and B to C,
BA ≅ BC.
So that applying <em>Pythagoras</em> theorem to ΔABD, we have:
= 
+ 
= 
+ 
= 
AB = 5 units
So that,
BA ≅ BC = 5 units
Therefore, it can be <u>concluded</u> that point D is <em>equidistant</em> from points A and C.
For more clarifications on a perpendicular bisector of a line, visit: brainly.com/question/929137
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