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fredd [130]
1 year ago
5

Use a graphing utility to graph the function and visually estimate the limits.

Mathematics
1 answer:
levacccp [35]1 year ago
8 0

The value of the \lim_{x \to 0} f(x) and \lim_{x \to \frac{\pi }{3} } f(x) are 0 and 1.153 .

<h3></h3><h3>What is the limiting value of a function?</h3>

Limiting Value of a Function. The function's limit is the value of the function as its independent variable, such as x approaches a certain value called the limiting value. For simple equations, this is similar to finding out the value of y when x has a unique value.

Given that,

f(x) = 4x cos x

First to calculate the limit value of the given function at x=0.

\lim_{x \to 0} f(x) = \lim_{x \to 0} 4x cosx

                   = 4×0×1                              (∵ cos0 = 1)

\lim_{x \to 0} f(x) = 0

Similarly,

\lim_{x \to \frac{\pi }{3} } f(x) = \lim_{x \to \frac{\pi }{3} } 4x cosx

                     =  4×\frac{\pi }{3}×cos\frac{\pi }{3}

                     =  4×\frac{\pi }{3}×\frac{1}{2}                          (∵cos60° = \frac{1}{2})

\lim_{x \to \frac{\pi }{3} } f(x)  = 1.153

Hence, The value of the \lim_{x \to 0} f(x) and \lim_{x \to \frac{\pi }{3} } f(x) are 0 and 1.153.

To learn more about the limit of the function from the given link:

brainly.com/question/23935467

#SPJ9

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Studentka2010 [4]

Answer:

1000 times

Step-by-step explanation:

Given:

The Sun is roughly 10^2 times as wide as the Earth.

The Star KW Sagittarii is roughly 10^5 times as wide as the Earth.

Question asked:

About how many times as wide as the Sun is KW Sagittarii?

Solution:

Let the width of the earth =  x

As the Sun is roughly 10^2 times as wide as the Earth, hence the width of the sun = x\times10^{2}

And as the Star KW Sagittarii is roughly 10^5 times as wide as the Earth, hence the width of the Star = x\times10^{5}

Now, to find that how many times width of the Star  KW Sagittarii is as respect to the width of the Sun, we will simply divide:

Width of the Star  KW Sagittarii =  x\times10^{5}

Width of the Sun = x\times10^{2}

\frac{x\times10^{5} }{x\times10^{2} }

x canceled by x

\frac{10^{5} }{10^{2} } =10^{5-2} =10^{3} =10\times\ 10\times10=1000

Therefore, Star  KW Sagittarii is 1000 times wider than Sun.

<em>First of all we calculated width of Sun in terms of width of earth and then calculated the width of the Star in terms of earth and for comparison we did simple division that showed that the Star KW Sagittarii is 1000 times wider than the Sun.</em>

<em />

4 0
3 years ago
The local school sponsored a mini-marathon and supplied 84 gallons of water per hour for the runners. What is the amount of wate
Dmitrij [34]
All you need to do is multiply 84 by 4. 

The number of gallons by the number of quarts <em>in a gallon. </em>

80*4= 320

4*4=16

320+16= 336

There are 336 quarts of water supplied an hour. 

I hope this helps!
~kaikers
3 0
3 years ago
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There are 12 donuts in a dozen. You are allowed to eat 2. How many different combinations of donuts could
Eddi Din [679]

Answer:

Step-by-step explanation:

8 0
3 years ago
Use the diagram below to find the value of each variable.
s2008m [1.1K]
Z=95° as opposite angles are equal
The angle next to 120° is 60° as angles on a straight line sum to 180°
This means that y=25° because angles in a triangle sum to 180°
Therefore x=155° as angles on a straight line sum to 180°
8 0
3 years ago
9. How many gallons of paint will you need to buy if you are painting a room that is 30 ft by
pentagon [3]

Answer:

To paint the room with dimension 30 ft by 50 ft by 50 ft is 26.67 gallon    

Step-by-step explanation:

Given as :

The Length of wall = L = 50 ft

The width of wall   = W = 30 ft

The height of wall  = H = 50 ft

Each gallon of paints should cover 300 sq feet

Let the amount o gallon required to paint the room = x

SO, Area of four wall = 2 × ( L + W ) × H

Or, Area of four wall = 2 × ( 50 + 30 ) × 50

Or, Area of four wall = 2 × ( 80 ) × 50

SO, Area of four wall = 8000  ft²

∵ To paint 300 sq ft the amount of paint required = 1 gallon

∴ To paint 8000 sq ft the amount of paint required = 26.67 gallon

Hence ,to paint the room with dimension 30 ft by 50 ft by 50 ft is 26.67 gallon      answer  

6 0
3 years ago
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