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wariber [46]
3 years ago
9

Determine whether the improper integral converges or diverges, and find the value of each that converges.

Mathematics
1 answer:
Ksju [112]3 years ago
8 0

Answer:converge at I=\frac{1}{3}

Step-by-step explanation:

Given

Improper Integral I is given as

I=\int^{\infty}_{3}\frac{1}{x^2}dx

integration of \frac{1}{x^2}  is  -\frac{1}{x}

I=\left [ -\frac{1}{x}\right ]^{\infty}_3

substituting value

I=-\left [ \frac{1}{\infty }-\frac{1}{3}\right ]

I=-\left [ 0-\frac{1}{3}\right ]

I=\frac{1}{3}

so the value of integral converges at \frac{1}{3}

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X^2 +6x+30 in vertex form
Elina [12.6K]

Answer:

Step-by-step explanation:

Factoring  x2-6x-30

The first term is,  x2  its coefficient is  1 .

The middle term is,  -6x  its coefficient is  -6 .

The last term, "the constant", is  -30

Step-1 : Multiply the coefficient of the first term by the constant   1 • -30 = -30

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   -6 .

     -30    +    1    =    -29

     -15    +    2    =    -13

     -10    +    3    =    -7

     -6    +    5    =    -1

     -5    +    6    =    1

     -3    +    10    =    7

     -2    +    15    =    13

     -1    +    30    =    29

7 0
3 years ago
Read 2 more answers
Give the first 4 terms of a sequence who has the explicit formula an = 4n – 13
andreev551 [17]

Step-by-step explanation:

from,

An = 4n -13

A1 = 4 (1) - 13

> A1 = -9

A2 = 4(2) - 13

> A2 = -5

A3 = 4(3) - 13

> A3 = -1

A4 = 4(4) - 13

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3 years ago
Write an exponential function to describe the given sequence of numbers, assuming that the first number in the sequence correspo
Fantom [35]

Answer:

y = 5(6) {}^{x}

Step-by-step explanation:

A exponential function is represented by

y = ab {}^{x}

where a is the vertical stretch and b is the base and x is the nth

power of x

Since the first number corresponds with zero, that means our y intercept is the first number.

This means when x=0 , y=5 so let find the value of 5.

5 = ab {}^{0}

b to the 0th power equal 1 so

5 = a \times 1

a = 5

Our equation is for now

y = 5b {}^{x}

Now let plug in 1,30

30 = 5b {}^{1}

Divide 5 by both sides

6 = b {}^{1}

Anything to the 1st power is itself so b equal 6.

So our equation is

y = 5(6) {}^{x}

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