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3 years ago

For the function f(x)=x^2-x determine f(x-2) in simplest form

Mathematics

1 answer:

tiny-mole [99]3 years ago

3 0

Easy, sub x-2 for x
f(x-2)=(x-2)^2-(x-2)
expand
f(x-2)=(x^2-2x-2x+4)-(x-2)
f(x-2)=(x^2-4x+4)-x+2
f(x-2)=x^2-5x+6

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Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent p-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

5 0

3 years ago

Pablo wants to build a rectangular pen for the pig he is raising in his agriculture class. Pablo only has 36 feet of fencing. Wh

Ratling [72]

Answer:

Area of the rectangular pen is: $18 \,x-x^2$

Step-by-step explanation:

We need to specify that the perimeter of the rectangular area of side x adds to the amount of fence Pablo has (36 feet). Recall as well that the opposite sides of a rectangle are equal, so if there is a side of length x, there must be another one of this size as well (a total of 2 x in the perimeter),let's assume that the perpendicular sides to x are of length y, then:

Perimeter= 2 x + 2 y = 36

so, 2 (x+y) = 36 then (x+y) = 18

and therefore the side y should be:

y = 18 - x

Now we can write the formula for representing the area of the rectangle (product of both quantities: x * y

$Area=x\,*\,y = x\,(18-x) =18 \,x-x^2$

4 0

3 years ago

Solve 5(x+9) - 4 = 71 for x

MrRissso [65]

Solving for x you would get X=6

7 0

3 years ago

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Sergeu [11.5K]

Answer:

f=9 x 20

Step-by-step explanation:

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Write an equation to represent the N'th term of the sequence (2,-1.-4,-7,...)

mr_godi [17]

Answer: a(n) = 5 - 3n

the sequence has:

a1 = 2

a2 = -1

a3 = -7

.........

we can see that: a2 - a1 = a3 - a2 = -3

=> the sequence is a arithmetic sequence

=> the distance between the numbers is d = -3

because this sequence is a arithmetic sequence

=> a(n) = a1 + (n - 1)d = 2 + (n - 1).(-3) = 5 - 3n

Step-by-step explanation:

7 0

3 years ago