<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:
D
Step-by-step explanation:
Just plug in the x values in the table to solve for the corresponding y value.
1. 3^2-11(3)+30
9-33+30
9-3
6
There is only one answer choice with 6 as the first number; thus, D is the correct answer.
4800 divide by 3=1600 (2 cars 1 truck)
4600-1600-3000 (6 cars)
3000 divide by 3 = 1000(2cars)
1000 times 2=2000(4 cars )
4800-2000-2800 (2 cars 3 trucks)
$2,800 is your answer
Answer:
V =41.41³
A = 94.41²
----
V =225.16³
SA =283.25²
----
V = 64³
SA =113.32²
----
V =433.33³
SA = 378.57²
Step-by-step explanation:
Picture 2 = a = 1/2 base = 3.5 x 3.5 = 12.25 b= 5 x 5 = 25
c²= a² + b² = 3.5² + 5²
c ²= √12.25 + √25
c ²= √ 37.5 = 6.12372435696
c ² = 6.1237 missing side
Picture 1 + 2 formula SA = bh + (s1 + s2 + s3)H
V = V= 1/2 b x h h x SA
Picture 3 + 4 formula SA= a²+ 2a a² / 4 + h² V= a² h/3
Answer:
x = 22, The length of BC is 22
Step-by-step explanation:
It is shown that angle ACB and angle ABC are congruent (The measure of angles are the same) in the picture. Since the angles are congruent, we can say that AC = AB because of base angle theorem converse. We can then substitute the given numbers in for AC and AB. We would then get 2x - 24 = x - 2. If you solve, you would get that x = 22 (The length of BC is 22).
