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pickupchik [31]
4 years ago
11

Find the limit, if it exists. (If an answer does not exist, enter DNE.)

Mathematics
1 answer:
Charra [1.4K]4 years ago
6 0

Note that your function can be written as

\begin{cases}\frac{2-(-x)}{2+x}&\text{if } x0\end{cases} = \begin{cases}\frac{2+x}{2+x}&\text{if } x0\end{cases} = \begin{cases}1&\text{if } x0\end{cases}

So, if x is negative, your function is identically equal to 1. In particular, the limit as x approaches -2 will be 1 as well.

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Geometry Find x and y given that the quadrilateral is a parallelogram
kherson [118]

Answer:

x = 3

y = 2

Step-by-step explanation:

Opposite side of parallelogram are equal.

-4x + 6 = -6x

-4x = -12x

-x = -3

x = 3

7y + 3 = 12y - 7

-5y = -10

-y = -2

y = 2

6 0
3 years ago
The fraction a/b is in simplest terms and equal to the following:((2020^3)-1)/((2021^3)+1) . What is a + b?
blagie [28]

Consider the expression

\dfrac{x^3-1}{(x+1)^3+1}

Factorize the numerator and denominator a difference/sum of cubes:

\dfrac{(x-1)(x^2+x+1)}{((x+1)+1)((x+1)^2-(x+1)+1)}

Expand the denominator:

\dfrac{(x-1)(x^2+x+1)}{(x+2)((x^2+2x+1)-(x+1)+1)}=\dfrac{(x-1)(x^2+x+1)}{(x+2)(x^2+x+1)}=\dfrac{x-1}{x+2}

since <em>x</em> = 2020, and clearly 2020² + 2020 + 1 ≠ 0, so we can cancel the factor of <em>x</em> ² + <em>x</em> + 1. This leaves us with

\dfrac{2020^3-1}{2021^3+1} = \dfrac{2020-1}{2020+2} = \dfrac{2019}{2022}=\dfrac{673}{674}=\dfrac ab

so that <em>a</em> + <em>b</em> = 673 + 674 = 1347.

7 0
3 years ago
I don't understand ÷ fractions
Reptile [31]
Ok. so, you have a fraction. lets say it is, 5/20. and the other, is. 2/5. flip the first one, and multiply. so your answer would be, 25/40. hope this helps.
7 0
3 years ago
Choose the correct conic section to fit the equation. X=1/16y^2
arsen [322]

Hello from MrBillDoesMath!

Answer:

Parabola

Discussion:

The equation is x = (1/16) y^2. Multiply both sides by 16 to get

y^2 = 16x is a parabola that "opens to the right". (Looks like y = x^2 rotated clockwise 90 degrees)

Thank you,

MrB


3 0
4 years ago
The Yu family and the Sainz family went on vacation together and each family leased a car. The leasing company charged a flat re
fenix001 [56]

Answer:

y= 0.15 and x=77.00

Step-by-step explanation:

6 0
4 years ago
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