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Dimas [21]
3 years ago
7

Limit question: lim x-->pi ((e^sinx)-1)/(x-pi)

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
4 0
\displaystyle\lim_{x\to\pi}\dfrac{e^{\sin x}-1}{x-\pi}

Notice that if f(x)=e^{\sin x}, then f(\pi)=e^{\sin\pi}=e^0=1. Recall the definition of the derivative of a function f(x) at a point x=c:

f'(c):=\displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}

So the value of this limit is exactly the value of the derivative of f(x)=e^{\sin x} at x=\pi.

You have

f'(x)=\cos x\,e^{\sin x}\implies f'(\pi)=\cos\pi\,e^{\sin\pi}=-1
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How many times smaller is 2 × 10^-10 than 4 × 10^-5
natta225 [31]

Answer:

200,000

Step-by-step explanation:

To find how many times smaller is smaller number than greater number, divide greater number by smaller number.

Greater number =4\times 10^{-5}

Smaller number =2\times 10^{-10}

Then

\dfrac{\text{Greater number}}{\text{Smaller number}}\\ \\=\dfrac{4\times 10^{-5}}{2\times 10^{-10}}\\ \\=\dfrac{4}{2}\times \dfrac{10^{-5}}{10^{-10}}\\ \\=2\times \dfrac{1}{10^{-5}}\\ \\=2\times 10^5\\ \\=2\times 100,000\\ \\=200,000

7 0
3 years ago
Find the length of the leg(s) of a right triangle, to the nearest hundredth, if both legs are equal and the hypotenuse is 10.
charle [14.2K]

Answer:

7.07 units

Step-by-step explanation:

Use the Pythagorean theorem for the right triangle:

\text{hypotenuse}^2=\text{leg}_1^2+\text{leg}_2^2,\\ \\c^2=a^2+b^2.

If a = x, b = x, and c = 10, then

10^2=x^2+x^2,\\ \\100=2x^2,\\ \\x^2=50,\\ \\x=\sqrt{50}=5\sqrt{2}\approx 7.07\ units.

7 0
3 years ago
The nutritional chart on the side of a box of a cereal states that there are 84 calories in a 3/4 cup serving. How many calories
pentagon [3]
<span>756=3/4x
x=1008 calories</span>
5 0
3 years ago
A newly launched clothing line is rapidly increasing in popularity. Every month 20% more items of clothing are sold. If 70,800 i
prohojiy [21]

Answer:

<u>212,400 items</u> were sold in 10 months.

Step-by-step explanation:

Given:

Items sold this month = 70,800

Percent Increase in every month = 20%

We need to find number of items sold in coming 10 months.

Solution:

First we will find number of items increase in each month.

number of items increase in each month can be calculated by Percent Increase in every month multiplied by Items sold this month and the divided by 100.

number of items increase in each month = \frac{20}{100} \times 70800 = 14,160

Now we will find number of item sold in 10 months.

number of item sold in 10 months is equal to sum of Items sold this month and number of items increase in each month multiplied by 10.

framing in equation form we get;

number of item sold in 10 months = 70800+10\times 14160 = 212,400

Hence <u>212,400 items</u> were sold in 10 months.

8 0
3 years ago
You aint even saying why is yes you chould try explaining it better next time.
olchik [2.2K]
What are you talking about?
3 0
2 years ago
Read 2 more answers
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