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3 years ago

which is a graph of f(x)=5x-2/x+2with any vertical or horizontal asympototes indicated by the dash lines?

Mathematics

1 answer:

Dahasolnce [82]3 years ago

7 0

Answer:

See attachment

Step-by-step explanation:

The given function is $f(x)=\frac{5x-2}{x+2}$ .

This rational function has a vertical asymptote at where the denominator is zero.

The denominator $x+2=0$ when $x=-2$

There is vertical asymptote at $x=-2$

The horizontal asymptote for this rational function is given by the ratio of the leading coefficient of the numerator to the leading coefficient of the denominator.

$y=\frac{5}{1}$

The horizontal asymptote is $y=5$

The graph of this rational function is shown in the attachment

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vichka [17]

Answer:

18 inches

Step-by-step explanation:

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2 years ago

Rewrite the following equation in standard form.<br><br> y= -2/7x + 5/8

nikitadnepr [17]

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3 years ago

Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx$

Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

$\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))$

Hence,

$SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}$

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3 years ago

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LekaFEV [45]

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3 years ago

Find the thirtieth term of the following sequence.

Nikolay [14]

You are adding 2 each time.

You are trying to find the 30th term, in which 4 are shown.

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30 - 4 = 26

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26 x 2 = 52

Add 52 to the last number given (0)

0 + 52 = 52

52 is your answer

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3 years ago

which is a graph of f(x)=5x-2/x+2with any vertical or horizontal asympototes indicated by the dash lines?​

which is a graph of f(x)=5x-2/x+2with any vertical or horizontal asympototes indicated by the dash lines?