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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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What is an equation of the line that passes through the point (1,-3) and is perpendicular to the line x+3y=21
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The linear equation that is perpendicular to the line x+3y=21 is:

y = 3*x - 6

<h3>How to find the equation of the line?</h3>

A general line in the slope-intercept form is written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

Two linear equations are perpendicular if the product between the two slopes is equal to -1.

Rewriting the given line we can get:

x +3y = 21

3y = 21 - x

y = 21/3 - x/3

y = (-1/3)*x + 21/3

Then the slope is (-1/3), if our line is perpendicular to this one, then:

m*(-1/3) = -1

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our line is:

y = 3*x + b

To find the value of b, we use the fact that our line passes through (1, - 3)

-3 = 3*1 + b

-3 - 3 = b

-6 = b

The line is y = 3*x - 6

Learn more about linear equations:

brainly.com/question/1884491

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3 0
1 year ago
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Step-by-step explanation:

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