1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mixer [17]
2 years ago
6

Find the limit

Mathematics
2 answers:
Lana71 [14]2 years ago
7 0

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}

muminat2 years ago
3 0

Answer:

Does not exist

Step-by-step explanation:

,, \lim_{x \to 1} \left[\frac{x-2}{x^{2}-x}-\frac{1}{x^{2}-3x^{2}+2x} \right] \\ \\ \lim_{x \to 1} \left[\frac{x-2}{x(x-1)}-\frac{1}{-2x(x-1)} \right] \\ \\ \lim_{x \to 1} \left[\frac{-2(x-2)}{-2x(x-1)}-\frac{1}{-2x(x-1)} \right] \\ \\ \lim_{x \to 1} \left[\frac{-2x+3}{-2x(x-1)} \right]

The limit doesn't exist.

You might be interested in
A copy machine makes 165 copies in three minutes and 45 seconds how many copies of them make per minute
NNADVOKAT [17]

So we just divide 165 by 3.75 to get 44 copies per minute.

4 0
3 years ago
Read 2 more answers
Can a repeating decimal can be written as an integer?
steposvetlana [31]
Yes a repeating decimal can be written as an integer
3 0
3 years ago
Read 2 more answers
Please please help me omg I give 28 points
Semmy [17]
No because all you have to do is subtract the discount and monthly plan. You get another number that is more.

Canvas is wack
4 0
3 years ago
Read 2 more answers
 55% of what number is 25
Valentin [98]
55% of a number is 25 so divide 25 by .55 then the answer is 45.45
4 0
3 years ago
Read 2 more answers
Help please.
gavmur [86]
I think the answer is 16.21 degrees
5 0
3 years ago
Other questions:
  • 100 points pls help
    9·1 answer
  • When turned about its axis of rotation, which shape could have created this three-dimensional object?
    7·2 answers
  • George wants to buy a shirt that costs $69.00. He has a 20% off coupon. How much will
    6·1 answer
  • On a piece of paper,graph y+4
    7·1 answer
  • The graph of 2 x − 5 y = 10 is shown on the grid. Which ordered pair is in the solution set of 2 x − 5 y ≥ 10?
    11·1 answer
  • 1. Miriam is starting a lawn mowing business. She bought a mower for $450 and will spend
    11·1 answer
  • Estimate to find the quotient. 342/8=
    9·1 answer
  • Dana found 6 rolls of yellow ribbon and green ribbon. Each roll of yellow ribbon was 1 meter long and each roll of green ribbon
    15·2 answers
  • An electrician completes 1/6 of a job in 2/3 hour. at this rate, how long does it take the electrician to complete the job?
    6·2 answers
  • A bookstore sells 7 books for $99.75. Which table represents the relationship between
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!