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Find the limit of the formula given​
find the limit of the formula given​ - 1

Answers

Answer 1
Answer:

Answer:

\displaystyle \lim_(x \to 0^+) x^\big{√(x)} = 1

General Formulas and Concepts:

Algebra II

  • Natural logarithms ln and Euler's number e
  • Logarithmic Property [Exponential]:                                                             \displaystyle log(a^b) = b \cdot log(a)

Calculus

Limits

  • Right-Side Limit:                                                                                             \displaystyle \lim_(x \to c^+) f(x)
  • Left-Side Limit:                                                                                               \displaystyle \lim_(x \to c^-) f(x)

Limit Rule [Variable Direct Substitution]:                                                             \displaystyle \lim_(x \to c) x = c

L’Hopital’s Rule:                                                                                                     \displaystyle \lim_(x \to c) (f(x))/(g(x)) = \lim_(x \to c) (f'(x))/(g'(x))

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹  

Step-by-step explanation:

We are given the following limit:

\displaystyle \lim_(x \to 0^+) x^\big{√(x)}

Substituting in x = 0 using the limit rule, we have an indeterminate form:

\displaystyle \lim_(x \to 0^+) x^\big{√(x)} = 0^0

We need to rewrite this indeterminate form to another form to use L'Hopital's Rule. Let's set our limit as a function:

\displaystyle y = \lim_(x \to 0^+) x^\big{√(x)}

Take the ln of both sides:

\displaystyle lny = ln \Big( \lim_(x \to 0^+) x^\big{√(x)} \Big)

Rewrite the limit by including the ln in the inside:

\displaystyle lny = \lim_(x \to 0^+) ln \big( x^\big{√(x)} \big)

Rewrite the limit once more using logarithmic properties:

\displaystyle lny = \lim_(x \to 0^+) √(x)ln(x)

Rewrite the limit again:

\displaystyle lny = \lim_(x \to 0^+) (ln(x))/((1)/(√(x)))

Substitute in x = 0 again using the limit rule, we have an indeterminate form in which we can use L'Hopital's Rule:

\displaystyle \lim_(x \to 0^+) (ln(x))/((1)/(√(x))) = (\infty)/(\infty)

Apply L'Hopital's Rule:

\displaystyle \lim_(x \to 0^+) (ln(x))/((1)/(√(x))) = \lim_(x \to 0^+) \frac{(1)/(x)}{\frac{-1}{2x^\big{(3)/(2)}}}

Simplify:

\displaystyle \lim_(x \to 0^+) \frac{(1)/(x)}{\frac{-1}{2x^\big{(3)/(2)}}} = \lim_(x \to 0^+) -2√(x)

Redefine the limit:

\displaystyle lny = \lim_(x \to 0^+) -2√(x)

Substitute in x = 0 once more using the limit rule:

\displaystyle \lim_(x \to 0^+) -2√(x) = -2√(0)

Evaluating it, we have:

\displaystyle \lim_(x \to 0^+) -2√(x) = 0

Substitute in the limit value:

\displaystyle lny = 0

e both sides:

\displaystyle e^\big{lny} = e^\big{0}

Simplify:

\displaystyle y = 1

And we have our final answer.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Limits

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Answers

Answer:x=13

Step-by-step explanation:

Since they are both corresponding angles you can create the equation

5x+21=86

Subtract 21 from each side

5x=65

Divide each side by 5

X=13

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Answers

It is answer b!!! hope this helps

A travel agency contacted a department store and obtained the list of all people who made purchases using their credit cards at the store in the last month. The agency then surveyed a random sample from the list, calling them to ask their preference for air travel or train travel for taking holidays. Which of the following types of bias affects the conclusions of the survey?a) Deliberate bias
b) Response bias
c) Non-response bias
d) Selection bias

Answers

Answer: Selection bias

Step-by-step explanation:

From the question, we are informed that a travel agency contacted a department store and obtained the list of all people who made purchases using their credit cards at the store in the last month. The agency then surveyed a random sample from the list, calling them to ask their preference for air travel or train travel for taking holidays.

The bus depicted above is referred to as the selection bias. The selection bias is simply a bias that is introduced when the sample obtained is not a representation of the population that the researcher wants to analyze. Here, the study population doesn't represent the target population.

The list gotten was for the people who made purchases using their credit cards but the agency used the list to determine the preference for air travel or train travel for taking holidays. This shows selection bias.

calculate the variance and standard deviation for the following samples set of data. 83.6,92.3,56.5,43.8,77.1,66.7. (Do not round intermediate calculation. Round your final answers and the nearest tenth.)​

Answers

Answer:

Variance: 322.4479999999996

Standard Deviation: 17.956837137981722

Final answer:

To calculate the variance and standard deviation for the given sample set of data, find the sample mean, calculate the squared differences, and then find the sample variance and standard deviation.

Explanation:

To calculate the variance and standard deviation for the given sample set of data (83.6, 92.3, 56.5, 43.8, 77.1, 66.7), follow these steps:

  1. Calculate the sample mean by adding all the values together and dividing by the total number of values: (83.6 + 92.3 + 56.5 + 43.8 + 77.1 + 66.7) / 6 = 69.8.
  2. Calculate the squared differences between each value and the sample mean: (83.6 - 69.8)^2, (92.3 - 69.8)^2, (56.5 - 69.8)^2, (43.8 - 69.8)^2, (77.1 - 69.8)^2, (66.7 - 69.8)^2.
  3. Calculate the sample variance by summing up the squared differences and dividing by (n-1), where n is the total number of values: (83.6 - 69.8)^2 + (92.3 - 69.8)^2 + (56.5 - 69.8)^2 + (43.8 - 69.8)^2 + (77.1 - 69.8)^2 + (66.7 - 69.8)^2 = 300.46. Sample variance = 300.46 / 5 = 60.1.
  4. Calculate the sample standard deviation by taking the square root of the sample variance: √60.1 = 7.79. Rounded to the nearest tenth, the sample standard deviation = 7.8.

Learn more about Calculating Variance and Standard Deviation here:

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Let X be the set of all 3×3 matrices whose diagonal entries are all 0. With the usual matrix addition and scalar multiplication, is X a vector space? (b) Let Y be the set of all 3 × 3 matrices whose diagonal entries add up to 0. With the usual matrix addition and scalar multiplication, is Y a vector space?

Answers

Answer:

Please see attachment

Step-by-step explanation:

Please see attachment

A calzone is divided into 24 equal pieces. Sophie and Glenn each ate one-fourthof the calzone on Saturday. The next​ day, Glenn ate one-sixth
of the calzone that was leftover. How many of the pieces of the original calzone ​remain? Explain your reasoning.

Answers

Answer:

10 pieces

Step-by-step explanation:

Total no. of pieces of calzone = 24

No of pieces of calzone eaten by sophie = 1/4 of Total no. of pieces of calzone  = 1/4 of 24 = (1/4)*24= 6 pieces.

No of pieces of calzone eaten by Glenn = 1/4 of Total no. of pieces of calzone  = 1/4 of 24 = (1/4)*24= 6 pieces.

Total no of pieces eaten by both of them on saturday = 12.

No of pieces of calzone left = 24-12 = 12

_______________________________________________

No of pieces of calzone eaten by Glenn on next day = 1/6 of Total no. of pieces of calzone  left= 1/6 of 12 = (1/6)*12= 2 pieces

No of pieces of calzone left now after Glenn ate 2 of them = 12-2 = 10.

Thus 10 pieces  of original calzone are left  .
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