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3 years ago

PLEASE HELP ME ANSWER THESE I DOMT UNDERSTAND THEM... PLEASE AND THANK YOU

Mathematics

1 answer:

insens350 [35]3 years ago

5 0

Answer:

Step-by-step explanation:

3 $\frac{3}{5ax_{3} }$

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Find the limit

Lana71 [14]

Step-by-step explanation:

<h3>Appropriate Question :-</h3>

Find the limit

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]$

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]$

On substituting directly x = 1, we get,

$\rm \: = \: \sf \dfrac{1-2}{1 - 1}-\dfrac{1}{1 - 3 + 2}$

$\rm \: = \sf \: \: - \infty \: - \: \infty$

which is indeterminant form.

Consider again,

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]$

can be rewritten as

$\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 3x + 2)}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 2x - x + 2)}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( x(x - 2) - 1(x - 2))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ {(x - 2)}^{2} - 1}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 2 - 1)(x - 2 + 1)}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)(x - 1)}{x(x - 2) \: (x - 1))}\right]$

$\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)}{x(x - 2)}\right]$

$\rm \: = \: \sf \: \dfrac{1 - 3}{1 \times (1 - 2)}$

$\rm \: = \: \sf \: \dfrac{ - 2}{ - 1}$

$\rm \: = \: \sf \boxed{2}$

Hence,

$\rm\implies \:\boxed{ \rm{ \:\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right] = 2 \: }}$

$\rule{190pt}{2pt}$

7 0

2 years ago

Read 2 more answers

The side lengths of the state flag of Colorado are in the ratio 2:3. If a flag is 12 feet long, what is

jekas [21]

Answer:

12 ft

Step-by-step explanation:

it's either 12 or 18, I have no idea :/

5 0

2 years ago

The price p, in dollars, of a specific ca that is x year old is modeled by the function p(x)=22,255(0.91)^x

uysha [10]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The price p, in dollars, of a specific car that is x year old is modeled by the function p(x)=22,255(0.91)^x

a) to determine the cost of a 2 year old car, we will substitute 2 for x in the given function. Therefore

p(2)=22,255(0.91)^2

p(2)=22,255 × 0.8281 = $18673.655

Approximately $18674

b) to determine the cost of a 7 year old car, we will substitute 7 for x in the given function. Therefore

p(7)=22,255(0.91)^7

p(2)=22,255 × 0.51676101936 = 11500.51648579693

Approximately $11501

c) 0.91 indicates exponential decay rate. It is a fixed percentage by which the value of the car decreases every year. It is determined by (1 - rate of decay)

7 0

2 years ago

Please help me with this.

vivado [14]

Answer:

the ancer is 1

Step-by-step explanation:

6 0

2 years ago

6.<br> Write in exponential form: log(3)81 = 4

earnstyle [38]

Answer:

$81 = {3}^{4}$

Step-by-step explanation:

$log_{3}(81) = 4 \\ \\ 81 = {3}^{4}$

4 0

3 years ago