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Gala2k [10]
1 year ago
13

What is limit of startfraction x cubed minus 1 over x minus 1 endfraction as x approaches 1?

Mathematics
1 answer:
iogann1982 [59]1 year ago
3 0

The value of the given limit lim ₓ → 1 (x³ - 1)/(x - 1) = <u>3</u>.

In the question, we are asked what is the limit of startfraction x cubed minus 1 over x minus 1 endfraction as x approaches 1, that is, lim ₓ → 1 (x³ - 1)/(x - 1).

Unique real numbers are limits in mathematics. Let us consider a real-valued function "f" and a real number "c", the limit is normally defined as lim ₓ → c f(x) = L. The phrase is to be understood as "the limit of f of x, as x approaches c equals L." The right arrow indicates that function f(x) approaches the limit L as x approaches c. The "lim" displays the limit.

The value of the given limit can be calculated as follows:

lim ₓ → 1 (x³ - 1)/(x - 1)

= lim ₓ → 1 (x³ - 1³)/(x - 1), Since 1³ = 1

= lim ₓ → 1 (x - 1)(x² + x + 1)/(x - 1) , using the formula: a³ - b³ = (a - b)(a² + ab + b²)

= lim ₓ → 1 (x² + x + 1), Cancelling (x - 1) in the numerator and the denominator, since x → 1, that is, x is approaching 1 and not equal to 1, implying that x - 1 ≠ 0.

= (1² + 1 + 1), Substituting x = 1, and removing the limit.

= 3.

Thus, the value of the given limit lim ₓ → 1 (x³ - 1)/(x - 1) = <u>3</u>.

Learn more about limits at

brainly.com/question/10434858

#SPJ4

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Answer:

8

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- (-2) is the same as + 2

-10 + 2 = -8

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Most everyday purchases at the store are labeled with the price of the item before sales tax. Which expression could
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The manufacturer offers a $125 rebate on photocopiers purchases before january 1. what is the nest cost of a $1,475 photocopier
Yuri [45]

Answer:

The net cost of the photocopier before january 1 is <u>$1350.</u>

Step-by-step explanation:

Given:

The manufacturer offers a $125 rebate on photocopiers purchases before january 1.

Now, to find the net cost of $1,475 photocopier before january 1.

Amount of rebate before January 1 = $125.

Cost of photocopier = $1,475.

So, to get the net cost of $1475 photocopier before january 1 we subtract the rebate from it:

\$1475-\$125

=\$1350.

Therefore, the net cost of the photocopier before january 1 is $1350.

6 0
3 years ago
The football team has a total of 350 jersey there are 150 medium-sized-jersey. Percent of jerseys are medium-sized-jerseys
liubo4ka [24]

Answer: 525

Step-by-step explanation:

if your looking for 150 percent of 350, the answer is 525 because....

150 x 350/ 100 =525

3 0
3 years ago
4. Amazon executives believe that at least 70% of customers would return a product 2 days after it arrives at their home. A samp
inysia [295]

Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0.1635 = 16.35% probability of a sample result with 68% or fewer returns prior to the third day.

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.  
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportions has mean \mu = p and standard error s = \sqrt{\frac{p(1 - p)}{n}}

In this problem:

  • Sample of 500 customers, hence n = 500.
  • Amazon believes that the proportion is of 70%, hence p = 0.7

The <u>mean and the standard error</u> are given by:

\mu = p = 0.7

s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.7(0.3)}{500}} = 0.0205

The probability is the <u>p-value of Z when X = 0.68</u>, hence:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.68 - 0.7}{0.0205}

Z = -0.98

Z = -0.98 has a p-value of 0.1635.

0.1635 = 16.35% probability of a sample result with 68% or fewer returns prior to the third day.

A similar problem is given at brainly.com/question/25735688

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