X8>2÷(3+22+1) ⋅ 2 help me plz

Determine whether the integral is convergent or divergent. ∫[infinity] 2 e^−1/x / x^2 dx : O Convergent O divergent If it is con

monitta

Let $f(x)=e^{-1/x}$ . Then $f'(x)=\frac1{x^2}e^{-1/x}>0$ for all $x\ge2$ , so $f$ is strictly increasing. As $x\to\infty$ , $e^{-1/x}\to e^0=1$ , so $f$ is bounded above by 1. This is to say,

$e^{-1/x}$

and the integral of $\frac1{x^2}$ converges over the same domain, so this integral must also converge by comparison.

We have, by setting $y=-\frac1x$ ,

$\displaystyle\int_2^\infty\frac{e^{-1/x}}{x^2}\,\mathrm dx=\int_{-1/2}^0e^y\,\mathrm dy=e^0-e^{-1/2}=1-\frac1{\sqrt e}$

8 0

2 years ago

The distance from Fort Worth to Fresno is 1,530 miles. If a cyclist maintains an average speed of 17 miles per hour, how many ho

Tju [1.3M]

The time take for the cyclist to travel from Fort Worth to Fresno is $90 \ hours$

Explanation:

It is given that the distance from Fort Worth to Fresno is 1,530 miles.

The average speed of the cyclist is 17 miles per hour.

The time travelled by the cyclist can be determined using the formula,

$Distance=Speed \times Time$

Substituting the value of distance and speed, we get,

$1530=17\times Time$

Dividing both sides by 17, we get,

$90 =Time$

Thus, the time take for the cyclist to travel from Fort Worth to Fresno is $90 \ hours$

3 0

3 years ago

Help I will gave u brilliant answer please help

JulsSmile [24]

Answer:

a) 15/8 b) 25/18

Step-by-step explanation:

a) First bring all the fractions to a common denominator (I'm going to use 8th's). 5/8 is already simplified, 1/2=4/8, and 3/4=6/8. Then, simply add the numerators and leave the denominator: $\frac{5+4+6}{8} =\frac{15}{8}$

Since this can not be simplified any further, your final answer is 15/8.

b) Start by bringing all the fractions to a common denominator (for this problem, we'll use 18th's). 2/3=12/18, 1/6=3/18, and 5/9=10/18. Then just add all the numerators and leave the denominator the same: $\frac{12+3+10}{18} = \frac{25}{18}$

Since this cannot be simplified further either, your final answer is 25/18.

Hope this helps! :)

4 0

1 year ago

Read 2 more answers

Given the cylinder enter the radius, enter diameter, enter the height than

Anna [14]

The diameter is 10 so it would be pi•radius squared 3.14•52sq or 3.14•10•2=78.54 the base of the circle is 78.54

6 0

3 years ago

A kite flying in the air has a 4-m line attached to it. Its line is pulled taut and casts a 3-m shadow. Find the height of the k

NNADVOKAT [17]

Answer:

2.6

Step-by-step explanation:

I used the a^2+b^2=c^2 to get this answer. I squared all the number given and got 16 and 9. Then I subtract them to get 7. Finally square 7 off and got 2.6 as the final answer

Hope this helped

$\sqrt{7} = 2.6$

3 0

2 years ago