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MrMuchimi
3 years ago
7

Please help! Need answered! Please and thank you.

Mathematics
1 answer:
salantis [7]3 years ago
4 0

Answer:

1.  lim x→0  7e^x  =7

2.  lim f(x) does not exist

f(3) = 5

3.  1/12

Step-by-step explanation:

f(x) = 7e^x

lim x→0  7e^x  =7

AS we can see from the graph  it is around 7

We know that e^0 =1  so 7*1 =7


2.  The limit does not exists, because approaching the limit from the left f(3-) is 3.  Approaching the limit from the right f(3+) is 5.  f(3) = 5  since there is a closed circle at 3 with a value of 5.


3.  f(x) = x^ 1/2

We take the derivative

f'(x) = 1/2 x^ (-1/2)

    = 1/2 1/( x^.5)

To find it at x=36

     =  1/2 * 1/( 36^.5)

    = 1/2 * 1/6

   = 1/12

Since they are not equal, the limit does not exist.

You might be interested in
Police Chase: A speeder traveling 40 miles per hour (in a 25 mph zone) passes a stopped police car which immediately takes off a
zubka84 [21]

Answer:

a. 18.34 s b. 327.92 m

Step-by-step explanation:

a. How long before the police car catches the speeder who continued traveling at 40 miles/hour

The acceleration of the car a in 10 s from 0 to 55 mi/h is a = (v - u)/t where u = initial velocity = 0 m/s, v = final velocity = 55 mi/h = 55 × 1609 m/3600 s = 24.58 m/s and t = time = 10 s.

So, a =  (v - u)/t =  (24.58 m/s - 0 m/s)/10 s = 24.58 m/s ÷ 10 s = 2.458 m/s².

The distance moved by the police car in 10 s is gotten from

s = ut + 1/2at² where u = initial velocity of police car = 0 m/s, a = acceleration = 2.458 m/s² and t = time = 10 s.

s = 0 m/s × 10 s + 1/2 × 2.458 m/s² (10)²

s = 0 m + 1/2 × 2.458 m/s² × 100 s²

s = 122.9 m

The distance moved when the police car is driving at 55 mi/h is s' = 24.58 t where t = driving time after attaining 55 mi/h

The total distance moved by the police car is thus S = s + s' = 122.9 + 24.58t

The total distance moved by the speeder is S' = 40t' mi = (40 × 1609 m/3600 s)t' =  17.88t' m where t' = time taken for police to catch up with speeder.

Since both distances are the same,

S' = S

17.88t' = 122.9 + 24.58t

Also, the time  taken for the police car to catch up with the speeder, t' = time taken for car to accelerate to 55 mi/h + rest of time taken for police car to catch up with speed, t

t' = 10 + t

So, substituting t' into the equation, we have

17.88t' = 122.9 + 24.58t

17.88(10 + t) = 122.9 + 24.58t

178.8 + 17.88t = 122.9 + 24.58t

17.88t - 24.58t = 122.9 - 178.8

-6.7t = -55.9

t = -55.9/-6.7

t = 8.34 s

So, t' = 10 + t

t' = 10 + 8.34

t' = 18.34 s

So, it will take 18.34 s before the police car catches the speeder who continued traveling at 40 miles/hour

b. how far before the police car catches the speeder who continued traveling at 40 miles/hour

Since the distance moved by the police car also equals the distance moved by the speeder, how far the police car will move before he catches the speeder is given by S' = 17.88t' = 17.88 × 18.34 s = 327.92 m

4 0
2 years ago
For pmalachi for answering my question
Nikolay [14]
I’m very confused lol.
5 0
2 years ago
The price of an item yesterday was $120 . Today, the price fell to $54 . Find the percentage decrease.
Nesterboy [21]

Answer:

magnitude of decrease = 120 - 54 = 66$

the percentage = (66/100)×100 = 66%

8 0
3 years ago
Find the solutions of the system y = –2x – 1 and y = 3–x–1.
sweet [91]

There are two intersection points (-1, 1) and (-2, 3), and the x coordinates are -1 and -2.

<h3>What is an exponential function?</h3>

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent y = a^x

where a is a constant and a>1

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two equations:

y = –2x – 1 and

\rm y = 3^{-x-1}

From the graph, we can see:

There are two intersection points:

(-1, 1) and (-2, 3)

The x coordinates are -1 and -2

x = -1, y = 1

x = -2, y = 3

Thus, there are two intersection points (-1, 1) and (-2, 3), and the x coordinates are -1 and -2.

Learn more about the exponential function here:

brainly.com/question/11487261

#SPJ1

5 0
2 years ago
Please answer fast The vertices of a rectangle are located at the coordinates (1, 4), (1, 5), (6, 5),
hammer [34]

Answer:

See below ~

Step-by-step explanation:

<u>Drawing the rectangle</u> (Refer attachment)

<u>Horizontal sides</u>

  • There are two x-values present : 1 and 6
  • Find the difference
  • 6 - 1 = 5
  • The horizontal sides of the rectangle are <u>5</u> units long

<u>Vertical sides</u>

  • Two y-values are present : 4 and 5
  • Find the difference
  • 5 - 4 = 1
  • The vertical sides of the rectangle are <u>1</u> unit long

<u>Perimeter</u>

  • 2(Horizontal side + Vertical side)
  • 2(5 + 1)
  • 2(6)
  • 12
  • The perimeter of the rectangle is <u>12</u> units

3 0
1 year ago
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