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Margarita [4]
3 years ago
5

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

vergent, evaluate it. (If the quantity diverges, enter DIVERGES.)
Mathematics
1 answer:
monitta3 years ago
8 0

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}

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ioda

Function would be f(x) = 5x+85

here, x= 15

5(15)+85 = 75+85 = $160

8 0
3 years ago
Please help, ty if you do :D
Dennis_Churaev [7]

Answer:

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3 0
3 years ago
Paula owns a shoe store in Los Angeles. Whenever she orders a new style of shoe, she orders 5 pairs of that style in each of the
suter [353]

She orders 5 pair in 5 different sizes:

5 x 5 = 25 pair

She orders 3 pair in 3 different sizes:

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7 0
3 years ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s
Jobisdone [24]

Answer:

f(x)=x^4-9x^2-50x-150

Step-by-step explanation:

Let f(x) be the polynomial function of minimum degree with real coefficients whose zeros are 5, -3, and -1 + 3i be f(x).

By the complex conjugate property of polynomials, -1-3i is also a root of this polynomial.

Therefore the polynomial in factored form is f(x)=(x-5)(x+3)(x-(-1+3i))(x-(-1+3i))

We expand to get:f(x)=(x^2-2x-15)(x^2+2x+10)

We expand further to get:\

f(x)=x^4-9x^2-50x-150

3 0
3 years ago
Suppose I am playing a sport that does not allow me to end a match in a tie​ (AKA I have to either win or​ lose). If my probabil
Leviafan [203]

Answer: The required probability is 0.3456.

Step-by-step explanation:

Since we have given that

Probability of winning at any given time = 0.6

Probability of losing at any given time = 1-0.6 = 0.4

Number of total matches = 5

Number of won matches = 3

So, using "Binomial distribution", we get that

P(X=3)=^5C_3(0.6)^3(0.4)^2\\\\P(X=3)=0.3456

Hence, the required probability is 0.3456.

6 0
3 years ago
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