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3 years ago

Find the exact value of the following limit: lim x approaches 0 e^6x... check photo above.

Mathematics

1 answer:

horrorfan [7]3 years ago

8 0

Substituting x = 0 directly gives the indeterminate form 0/0, so you can use l'Hopital's rule (and you'll have to do that twice):

$\displaystyle\lim_{x\to0}\frac{e^{6x}-6x-1}{x^2}=\lim_{x\to0}\frac{6e^{6x}-6}{2x}=\lim_{x\to0}\frac{36e^{6x}}2$

The limand is continuous everywhere, so you can plug in x = 0 to get 36•1/2 = 18.

You might be interested in

Find next two terms. -162, -54, -18, ?, ?

STALIN [3.7K]

Answer:

-6, -2

Step-by-step explanation:

-2 ×3 = -6

-6 ×3 = -18

-18 x3 = -54

-54 x3 = -162

6 0

2 years ago

The difference of the squares of two positive consecutive even integers is 28. find the integers.

Klio2033 [76]

The integers are 8 and 6:

${8}^{2} - {6}^{2} = 64 -36 = 28$

7 0

3 years ago

I need help with the numbers 9 and 10 please help

Katen [24]

9] Rocky Falls would be 13.4°F at sunrise.

Use the equation 23.1 + (-9.7) = x, where x is the temperature at sunrise (13.4)
23.1 + (-9.7) = 23.1 - 9.7
Solve so that x = 13.4

10] Jamie originally had $263.25 in her account.

Just add how much she spent (135.75 + 32) to how much she ended up with (95.5)

135.75 + 95.5 + 32 = 263.25

If you are asking how much she has if she started out with $95.50 before going to the Mets game,

95.5 - (135.75 + 32) = -$72.25
Or 95.5 - 135.75 - 32, same result of -72.25

3 0

4 years ago

Identify the following sequences as arithmetic, geometric, or neither. For the arithmetic and geometric sequences, identify the

Lapatulllka [165]

Hence,

a. 12, 144, 1728,.. => Geometric

b. 0,5, 10, 15, 20, 25,... => Arithmetic

c. 0,4, 16, 36, 64,... => Neither arithmetic nor geometric

d. 1.5, 2.25, 3.375, 5.0625,... => Geometric

Step-by-step explanation:

In order to identify the sequence as geometric or arithmetic sequence, we find the common difference and common ratio of the sequence. If the common difference is same, it is an arithmetic sequence and if the common ratio is same the sequence is a geometric sequence

Common difference is the difference between consecutive terms of an arithmetic sequence and common ration is the ratio between two consecutive terms of a sequence

So,

a. 12, 144, 1728,..

Here,

$a_1=12\\a_2=144\\a_2=1728$

Common difference:

$d=a_2-a_1 = 144-12 = 132\\=a_3-a_2 = 1728-144=1584$

Common Ratio:

$r=\frac{a_2}{a_1} =\frac{144}{12} = 12\\=\frac{a_3}{a_2}=\frac{1728}{144} =12$

As the common ratio is same, the given sequence is a geometric sequence.

b. 0,5, 10, 15, 20, 25,...

Here,

$a_1 = 0\\a_2 =5\\a_3 =10$

Common difference:

$d=a_2-a_1 = 5-0 = 5\\d=a_3-a_2 = 10-5 = 5$

As the common difference is same, the given sequence is an arithmetic sequence

c. 0,4, 16, 36, 64,...

Here

$a_1 = 0\\a_2 =4\\a_3 = 16\\a_4 = 36$

Common Difference:

$d= a_2-a_1 = 4-0 = 4\\a_3-a_2 = 16-4 = 12$

Common Ratio:

$r=\frac{a_2}{a_1} = \frac{4}{0} = Doesn't\ exist$

Neither the common ratio nor common difference are same, so the given sequence is neither arithmetic nor geometric

d. 1.5, 2.25, 3.375, 5.0625,...

Here

$a_1 = 1.5\\a_2 = 2.25\\a_3 = 3.375$

Common Difference:

$d=a_2-a_1 = 2.25-1.5 = 0.75\\a_3-a_2 =3.375-2.25 = 1.125[/tex]Common Ratio: [tex]r=\frac{a_2}{a_1} = \frac{2.25}{1.5}=1.5\\=\frac{a_3}{a_2} =\frac{3.375}{2.25}=1.5$

As the common ratio is same, given sequence is geometric

Hence,

a. 12, 144, 1728,.. => Geometric

b. 0,5, 10, 15, 20, 25,... => Arithmetic

c. 0,4, 16, 36, 64,... => Neither arithmetic nor geometric

d. 1.5, 2.25, 3.375, 5.0625,... => Geometric

Keywords: Sequence, Ratio

Learn more about sequences at:

#LearnwithBrainly

4 0

3 years ago

The velocity of a car was 30m/s when the driver pushed the brake of the car and it stopped after 2 seconds. Assume that the acce

Murljashka [212]

Answer:

the "acceleration" is -15m/s (it's negative because it is slowing down, not speeding up[it might just be a positive 15m/s if it is called deceleration and not acceleration])

Step-by-step explanation:

30m/s (starting speed)/2 (the number of seconds it took to stop from 30m/s

3 0

3 years ago

Find the exact value of the following limit: lim x approaches 0 e^6x... check photo above.​

Find the exact value of the following limit: lim x approaches 0 e^6x... check photo above.