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aksik [14]
3 years ago
13

How do you find the limit of (2+x)^3 -8/x as the limit approaches 0? Please explain how you did it.​

Mathematics
1 answer:
RoseWind [281]3 years ago
5 0

Answer:  12

<u>Step-by-step explanation:</u>

Expand (2 + x)³, factor out the x, then replace x with zero.

(x+2)^3 = (x+2)(x+2)(x+2)\\.\qquad \quad =(x+2)(x^2+4x+4)\\.\qquad \quad =x(x^2+4x+4)+2(x^2+4x+4)\\.\qquad \quad =x^3+4x^2+4x\quad +2x^x+8x+8\\.\qquad \quad =x^3+(4x^2+2x^2)+(4x+8x)+8\\.\qquad \quad =x^3+6x^2+12x+8

\dfrac{(x+2)^3-8}{x}=\dfrac{(x^3+6x^2+12x+8)-8}{x}=\dfrac{x^3+6x^2+12x}{x}\\\\\\=\dfrac{x(x^2+6x+12)}{x}=x^2+6x+12\\\\\\ \lim_{x \to 0} \quad x^2+6x+12\quad =\quad 0+0+12\quad =\quad \large\boxed{12}

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3 years ago
Gabrielle uses 7.6 pints of blue paint and white paint to paint her bedroom walls. 1 4 of this amount is blue paint, and the res
zysi [14]

Answer:

1.9

Step-by-step explanation:

Gabrielle uses 7.6 pints of blue and white paint to paint her bedroom

1/4 of the paint is blue paint

Therefore the amount of white paint she used to paint her bedroom can he calculated as follows

= 1/4

= 0.25×100

= 25%

25/100×7.6

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3 years ago
Which statements about angles are true? Check all that apply.
Vadim26 [7]

Answer:

A,C,D,E

Step-by-step explanation:

The first one is true because in fact, supplementary angles' measures add up to 180°.

The second one is false because there are 5 types, not 3. These are the types:

acute angle-an angle between 0 and 90 degrees.

right angle-an 90 degree angle.

obtuse angle-an angle between 90 and 180 degrees.

straight angle-a 180 degree angle.

reflex angle- a angle between 180 and 360 degrees.

Third is true too because linear pair means two angles that form a straight line, or 180°.

Fourth is true because straight Angle theorem states that all the straight angles are 180 degrees. If the legs are pointing exactly in the opposite directions, then it forms a straight angle.

Last one is true because by definition complementary angles always form a right angle, which is 90°.

Hope it helps!

8 0
3 years ago
Which simplified fraction is equal to 0.53 with the three repeating?
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Answer:

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answer is 8/15

8 0
3 years ago
South School has a circular pattern on the playground that has a radius of 6 feet. Find a. the circumference of the pattern and
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Answer:

Circumference: 37.68

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Step-by-step explanation:

the formula to find the circumference is 2 x 3.14 x r

r is the radius so you plug in 6 for that

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the formula to find the area of a circle is 3.14 x r ²

r is still the radius so you plug in 6 for that

3.14 x 6² = 113.04

6 0
3 years ago
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