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2 years ago

1. Which graph shows y as a function of x?

Mathematics

1 answer:

katen-ka-za [31]2 years ago

8 0

Answer:

Step-by-step explanation:

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Use the definition of continuity and the properties of limit to show that the function f(x)=x sqrtx/ (x-6)^2 is continuous at x=

jasenka [17]

Answer:

The function $\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$ is continuous at x = 36.

Step-by-step explanation:

We need to follow the following steps:

The function is:

$\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$

The function is continuous at point x=36 if:

The function $\\ f(x)$ exists at x=36.
The limit on both sides of 36 exists.
The value of the function at x=36 is the same as the value of the limit of the function at x = 36.

Therefore:

The value of the function at x = 36 is:

$\\ f(36) = \frac{36*\sqrt{36}}{(36-6)^{2}}$

$\\ f(36) = \frac{36*6}{900} = \frac{6}{25}$

The limit of the $\\ f(x)$ is the same at both sides of x=36, that is, the evaluation of the limit for values coming below x = 36, or 33, 34, 35.5, 35.9, 35.99999 is the same that the limit for values coming above x = 36, or 38, 37, 36.5, 36.1, 36.01, 36.001, 36.0001, etc.

For this case:

$\\ lim_{x \to 36} f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$

$\\ \lim_{x \to 36} f(x) = \frac{6}{25}$

Since

$\\ f(36) = \frac{6}{25}$

And

$\\ \lim_{x \to 36} f(x) = \frac{6}{25}$

Then, the function $\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$ is continuous at x = 36.

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3 years ago

I need help with 1 2 3

g100num [7]

D D B I think this should be right

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2 years ago

Xiang is a teacher who bought a $2350 laptop for school use. The laptop is an allowable

Nata [24]

Answer:

Step-by-step explanation:

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3 years ago

Although the actual amount varies by season and time of day, the average volume of water that flows over the falls each second

lutik1710 [3]

Given that the average volume of water that flows over the falls each second is $4.8 \times 10^5$ gallons.

There are 3,600 seconds in one hour.

Thus, in one hour, $4.8 \times 10^5\times3600=17280\times10^5=1.728\times10^9$ gallons of water flows over the falls.

Therefore, the amount of water that flows over the falls is $1.728\times10^9$ .

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2 years ago

What is the lateral area of this regular octagonal pyramid?

Murrr4er [49]

Answer:

229.7

Step-by-step explanation:

8 * 1/2 * 5.8 * 7 * sqrt(2.)

8 0

2 years ago

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1. Which graph shows y as a function of x?​

1. Which graph shows y as a function of x?