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sineoko [7]
3 years ago
12

Find the values of x (if any) at which f(x)= x+1/x^2-1 is not continuous. If so, is the discontinuity removable?

Mathematics
1 answer:
Mkey [24]3 years ago
8 0

f(x)=\dfrac{x+1}{x^2-1} has two points of discontinuity at x=\pm1, where x^2-1=0.

We have

\dfrac{x+1}{x^2-1}=\dfrac{x+1}{(x+1)(x-1)}

so as long as x\neq-1, we can cancel x+1 and be left with \dfrac1{x-1}. Then as x\to-1, we have

\displaystyle\lim_{x\to-1}f(x)=\lim_{x\to-1}\frac1{x-1}=-\frac12

The limit exists, so the discontinuity at -1 is removable (so definitely not C or D).

Meanwhile,

\displaystyle\lim_{x\to1}f(x)=\lim_{x\to1}\frac1{x-1}

does not exist, so the discontinuity at 1 is non-removable, making A the correct answer.

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Step-by-step explanation:

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6 0
3 years ago
Y = -3 + 1/2x 3x + 2y = 2<br><br><br> Help ASAP this is due today
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7 0
3 years ago
Can the sides of a triangle have lengths 3.5, 10.9, and 14.4?
andrew11 [14]

Answer:

No

Step-by-step explanation:

A triangle can NOT have those lengths because any side of a triangle has to have a length greater than the sum of the other two sides. In this case, 14.4, one of the sides, is not greater than the sum of the other two sides (which is also 14.4).

Hope this helps :)

4 0
2 years ago
What is the total surface area of the figure shown?
4vir4ik [10]

Given:

Composite figure.

The figure splitted into two shapes.

One is vertical cuboid and other is horizontal cuboid

To find:

Total surface area of the figure

Solution:

<u>Vertical cuboid:</u>

Length = 14 inches

Width = 12 inches

Height = 24 inches

Surface area = 2(lw + wh + lh)

                     = 2(14 × 12 + 12 × 24 + 14 × 24)

                     = 2(168 + 288 + 336)

Surface area = 1584 square inches

<u>Horizontal cuboid:</u>

Length = 14 inches

Width = 10 inches

Height = 30 - 12 = 18 inches

Surface area = 2(lw + wh + lh)

                     = 2(14 × 10 + 10 × 18 + 14 × 18)

                     = 2(140 + 180 + 252)

Surface area = 1144 square inches

Total surface area = 1584 + 1144

                              = 2728 square inches

The total surface area of the figure is 2728 square inches.

4 0
3 years ago
Need help its hard sadly
Maslowich
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8 0
3 years ago
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