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The limit as h approaches 0 of (e^(2+h)-e^2)/h is ?

Whitepunk [10]

If you plug in 0, you get the indeterminate form 0/0. You can, therefore, apply L'Hopital's Rule to get the limit as h approaches 0 of e^(2+h),
which is just e^2.
[e^(2+h) − e^2]/h = [e^2(e^h−1)]/h

so in the limit, as h goes to 0, you'll notice that the numerator and denominator each go to zero (e^h goes to 1, and so e^h-1 goes to zero). This means the form is 'indeterminate' (here, 0/0), so we may use L'Hoptial's rule:

=e^2

3 0

3 years ago

A number is multiplied by 3. If 3 is subtracted from the product you get 24.

vladimir1956 [14]

Nine is the answer cuz it equals 27 then subtract 2 equals 24

3 0

3 years ago

Read 2 more answers

The tile along the edge of a triangular community pool needs to be replaced. A right triangles, where the hypotenuse is labeled

jolli1 [7]

Perimeter of a closed figure is the sum of length of its outline. The perimeter of the consider triangular pool is: $12x^2 + 8x + 25$ units.

<h3>How to calculate perimeter of a triangular figure?</h3>

Perimeter of a triangle = Sum of lengths of all its 3 sides.

For the given case, we have:

Length of first side(hypotenuse) = $8x^2$ units

Height = $4x^2 + 15$ units

Base is of length $8x + 10$

Thus, its perimeter is calculated as:

Perimeter of a triangle = Sum of lengths of all its 3 sides.

Perimeter = $8x^2 + 4x^2 + 15 + 8x + 10 = (8+4)x^2 + 8x + 25 = 12x^2 + 8x + 25$ units

Perimeter = $12x^2 + 8x + 25$ units

Thus,

The perimeter of the consider triangular pool is: $12x^2 + 8x + 25$ units.

Learn more about perimeter here:

brainly.com/question/10466285

3 0

2 years ago

A company has 200 employees. The company’s owner randomly chose 30 employees for an in-depth survey. Of those surveyed, 12 emplo

andrey2020 [161]

(this shows the percent of people that would work over time on a regular basis out of the 30 people) 12/30= (40%) of the 30 said they would work overtime.

200×.4=80 employees of the 200 would have probably have said they would work overtime.

8 0

3 years ago

a) Work out the next term in this sequence. 4 12 16 b) Describe the rule for continuing this sequence. 44 41 38 35 32 c) The seq

horsena [70]

Answer:

1. Next sequence = 20

2. Tn = 47 - 3n

3. Common number: 32

Step-by-step explanation:

Given

Sequence 1: 0, 4, 8, 12, 16

Sequence 2: 44, 41, 38, 35, 32

a. Write out the next sequence in (1)

The pattern followed by sequence 1 is that, each successive sequence is and addition of 4 to the previous sequence..

See observation below

4 = 0 + 4

8 = 4 + 4

12 = 8 + 4

16 = 12 + 4

Definitely, the next sequence will be 4 + the previous sequence.

Next sequence = 16 + 4

Next sequence = 20

2. The rule for continuing sequence 2

It'll be observed that sequence 2 follows an arithmetic progression.

To get the rule for continuing the sequence, the following data are needed.

I. The first term of the sequence.

This is often represented by letter a.

a = 44

II. The common difference.

This is the difference between two successive sequence

This is often represented by letter d.

d = 41 - 44 = -3

Or

d = 38 - 44 = -3

Using the arithmetic progression formula

Tn = a + (n - 1)d

By substituting 44 for a and -3 for d.

Tn = 44 + (n - 1)(-3)

Tn = 44 - 3n + 3

Tn = 44 + 3 - 3n

Tn = 47 - 3n

Hence, the rule for continuing the sequence is 47 - 3n where n is the current term of the sequence

III. Work out a number in common in both sequence

It'll be observed that the visible data of sequence 2 are bigger than that of sequence 1.

To get a common number, we have to extend sequence 1 until we arrive at a common number in both sequence

Sequence 1: 0, 4, 8, 12, 16

This becomes

Sequence 1: 0, 4, 8, 12, 16, 20, 24, 28, 32.....

32 is common in sequence (1) and (2).

If the sequence is extended, we'll arrive at another common number. But we have to stop, since we've arrived at a common number.

3 0

3 years ago