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Zinaida [17]
3 years ago
11

Evaluate the limit. lim n > [infinity] 9n^3 +5n - 2n/ 2n^3

Mathematics
1 answer:
expeople1 [14]3 years ago
7 0

Answer:

The value of the limit is \frac{9}{2}

Step-by-step explanation:

When we are working with limits in which the variable goes to infinity, we only take the highest order factor of the numerator and of the denominator.

So we have

$\lim_{t \to +\infty} \frac{9n^{3}}{2n^{3}}$

We can simplify the cubes.

$\lim_{t \to +\infty} \frac{9}{2}$

The limit of a constant is the proper constant.

So the value of the limit is \frac{9}{2}

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Find the equation of the line tangent to the graph of
garik1379 [7]

Answer:

\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}

Step-by-step explanation:

We want to find the equation of the line tangent to the graph of:

\displaystyle y=\sin^{-1}\big(\frac{x}{5}\big)\text{ at } x=\frac{5}{2}

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

\displaystyle y^\prime=\frac{1}{\sqrt{1-(\frac{x}{5})^2}}\cdot\frac{1}{5}

Simplify:

\displaystyle y^\prime=\frac{1}{5\sqrt{1-\frac{x^2}{25}}}

We can factor out the denominator within the square root:

\displaystyle y^\prime =\frac{1}{5\sqrt{\frac{1}{25}\big(25-x^2)}}

Simplify:

\displaystyle y^\prime=\frac{1}{\sqrt{25-x^2}}

So, we can find the slope of the tangent line at <em>x</em> = 5/2. By substitution:

\displaystyle y^\prime=\frac{1}{\sqrt{25-(5/2)^2}}

Evaluate:

\displaystyle y^\prime=\frac{1}{\sqrt{75/4}}=\frac{1}{\frac{5\sqrt{3}}{2}}=\frac{2\sqrt{3}}{15}

We will also need the point at <em>x</em> = 5/2. Using our original equation, we acquire that:

\displaystyle y=\sin^{-1}(\frac{1}{2})=\frac{\pi}{6}

So, a point is (5/2, π/6).

Finally, by using the point-slope form, we can write:

\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}(x-\frac{5}{2})

Distribute:

\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}x+\frac{-\sqrt{3}}{3}

Isolate. Hence, our equation is:

\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}

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3 years ago
If A = ½ bh, what is the value of A if b = 5 and h = 8? Please help!!!!
tigry1 [53]

Answer: 20

Work: A = 1/2 bh

A = 1/2 (5(8))

A = 1/2 (40)

a = 20

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3 years ago
Read 2 more answers
Apply the distributive property to create an equivalent expression.<br> −9⋅(5j+k)=
Iteru [2.4K]

Multiply the number outside the parenthesis by each term inside the parenthesis:

-9 * 5j = -45j

-9 *k = -9k

−9⋅(5j+k) = -45j - 9k

3 0
2 years ago
Read 2 more answers
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