1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SIZIF [17.4K]
3 years ago
8

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=

36.

Mathematics
1 answer:
jasenka [17]3 years ago
8 0

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:

  1. The function \\ f(x) exists at x=36.
  2. The limit on both sides of 36 exists.
  3. 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.

You might be interested in
The mean is usually the preferred measure of central tendency, but there are specific situations in which it is impossible to co
sergey [27]

Answer: a. It is commonly referred to as the arithmetic average.

b. It is algebraically defined (that is, there is an equation you can use to calculate its value).

c. It is easily influenced by extreme scores.

Step-by-step explanation:

The mean is also referred to as the "average" and it is gotten by adding every number and the dividing the value gotten by the number of the numbers used for the calculation.

It should be noted that the mean is algebraically defined and can be easily influenced by extreme scores.

4 0
3 years ago
After a storm, two street lights with the same length are leaning against each
Ray Of Light [21]

Answer:

c = 4.79 feet

Step-by-step explanation:

Given question is incomplete without a picture; find the question with the attachment.

Two poles AD and DB of same length are leaning against each other.

Distance between the poles (AB) = 45 feet

m(∠ADB) = 180°- (60 + 50)°

               = 70°

By sine rule,

\frac{sin50}{AD}=\frac{sin70}{45}=\frac{sin60}{DB}

AD=\frac{45\times (sin50)}{sin70}

      = 36.68 ft

Similarly,

DB = \frac{45\times sin60}{sin70}

     = 41.47 ft

Now c = DB - AD

           = 41.47 - 36.68

           = 4.79 feet

4 0
3 years ago
F(x)=2(x+1)^2-2 What is the vertex
Bumek [7]

Answer:

(-1,-2)

Step-by-step explanation:

Let's bring back to memory vertex formula for parabolas.

y=a(x-h)^{2}+k

Where (h,k) is the vertex.

In f(x)=2(x+1)^{2}-2

The vertex is (-1,-2)

8 0
3 years ago
Keisha is making potato casserole
lord [1]

Answer:

4 1/2 I think

Step-by-step explanation:

I think but I'm not for sure

4 0
2 years ago
A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The comp
Dmitry [639]

Answer:

the correct graph of this function is a graph of a line that has a y-intercept that is approximately negative $20 million and an x-intercept that is approximately 2.7 years.

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Polygon ABCD will be dilated by a scale factor of 2.2 with the origin as the center of dilation, resulting in the image A'B'C'D'
    13·2 answers
  • Consider the differential equation dydx=6x, dydx=6x, with initial condition y(0)=4y(0)=4.
    9·1 answer
  • Given the parent function f(x) = 2x, which graph shows f(x) − 1?
    8·1 answer
  • Simplify: - 3/2(4x + 3)
    15·1 answer
  • kim is saving monyfor a trip this summer. She already has some money in her savings account and will add the same amount to her
    13·1 answer
  • True/ False: a sample of 100 fuses from a very large shipment is found to have 10 that are defective. The 95% confidence interva
    7·1 answer
  • What is -4 = -3 + x 8
    13·1 answer
  • I need answers for A -F
    15·1 answer
  • Please help no link please help no links
    12·1 answer
  • What is the simplified form of √45
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!