<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:
11) c = 16.1
12) c = 11.4
Step-by-step explanation:
11)
a² + b² = c²
8² + 14² = c²
64 + 196 = c²
c² = 260
c = 16.1
12)
a² + b² = c²
7² + 9² = c²
49 + 81 = c²
c² = 130
c = 11.4
Answer <span>B.X= 3 1/8
</span><span>X+7/8=4
x = 4 - 7/8
x =3 8/8 - 7/8
x = 3 1/8</span>
Answer:
<em>B) Kara's highest speed was between 30 and 35 minutes.</em>
Step-by-step explanation:
A zero slope (horizontal line) means a stopped car with zero speed.
The higher the slope, the steeper the line, the higher the speed.
Let's look at the options.
a) The car was stopped between 10 and 15 minutes, not 20. False.
b) Between 30 and 35 min, the graph shows the steepest slope, so this statement is True.
c) False, since here slope is not steepest.
d) Between 5 and 10 minutes, the graph is a straight line, so speed was constant. False.
Angle m∠1 if formed by a tangent and secant intersecting outside of circle. The intercepted arcs are arc LK and arc JK.
Thus;
Angle formed by Tangent and secant
=1/2(DIFFERENCE of Intercepted Arcs)
m∠1=1/2(mJK-LK)
Answer: m∠1=1/2(mJK-KL)
