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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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The perimeter of the tennis court is 228 feet. what are the dimensions of the court?
julsineya [31]
From a reliable source, the ratio between the width and the length of the tennis court is equal to 5:12. We let x be the common factor of the given ratio such that the width is equal to 5x and the length is equal to 12x. 

The perimeter of the figure is calculated through the equation,
              P = 2L + 2W
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Substituting the derived expressions to the equation above.

             228 = (2)(12x) + 2(5x)
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The width and length are calculated below.
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Answer:

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Step-by-step explanation:

the square of the sum of a number and 4

x^2+4

is means equals

x^2+4 = 36

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