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3 years ago

If f(x) = ln(2), then limx--->2 (f(2)-f(x))/x-2

Mathematics

1 answer:

Blizzard [7]3 years ago

7 0

Answer:

as written, -2
with denominator parentheses, 0
with f(x)=ln(x) and denominator parentheses, -1/2

Step-by-step explanation:

The problem as stated asks for the limit as x approaches 2 of (0/x) -2.

As written, the limit is (0/2) -2 = -2.

Explanation: f(x) is a constant, so the numerator is 0. The ratio 0/x -2 is defined as -2 everywhere except x=0. So, the value at x=2 is 0/2 -2 = -2.

If you mean (f(2) -f(x))/(x -2), that limit is the limit of 0/(x-2) = 0 as x approaches 2.

Explanation: f(x) is a constant, so the numerator is 0. The ratio 0/(x-2) is zero everywhere except at x=2. The left limit and right limit are both 0 as x approaches 2. Since these limits agree, the limit is said to be 0.

If you mean f(x) = ln(x) and you want the limit of (f(2) -f(x))/(x -2), that value will be -1/2.

Explanation: The value of the ratio is 0/0 at x=2, so we can find the limit using L'Hôpital's rule. Differentiating numerator and denominator, we have ...

lim = (-1/x)/(1)

The value is -1/2 at x=2.

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Consider a sample with data values of 27, 24, 21, 16, 30, 33, 28, and 24. Compute the 20th, 25th, 65th, and 75th percentiles. 20

densk [106]

Answer:

$P_{20} = 20$ --- 20th percentile

$P_{25} = 21.75$ --- 25th percentile

$P_{65} = 27.85$ --- 65th percentile

$P_{75} = 29.5$ --- 75th percentile

Step-by-step explanation:

Given

27, 24, 21, 16, 30, 33, 28, and 24.

N = 8

First, arrange the data in ascending order:

Arranged data: 16, 21, 24, 24, 27, 28, 30, 33

Solving (a): The 20th percentile

This is calculated as:

$P_{20} = 20 * \frac{N +1}{100}$

$P_{20} = 20 * \frac{8 +1}{100}$

$P_{20} = 20 * \frac{9}{100}$

$P_{20} = \frac{20 * 9}{100}$

$P_{20} = \frac{180}{100}$

$P_{20} = 1.8th\ item$

This is then calculated as:

$P_{20} = 1st\ Item +0.8(2nd\ Item - 1st\ Item)$

$P_{20} = 16 + 0.8*(21 - 16)$

$P_{20} = 16 + 0.8*5$

$P_{20} = 16 + 4$

$P_{20} = 20$

Solving (b): The 25th percentile

This is calculated as:

$P_{25} = 25 * \frac{N +1}{100}$

$P_{25} = 25 * \frac{8 +1}{100}$

$P_{25} = 25 * \frac{9}{100}$

$P_{25} = \frac{25 * 9}{100}$

$P_{25} = \frac{225}{100}$

$P_{25} = 2.25\ th$

This is then calculated as:

$P_{25} = 2nd\ item + 0.25(3rd\ item-2nd\ item)$

$P_{25} = 21 + 0.25(24-21)$

$P_{25} = 21 + 0.25(3)$

$P_{25} = 21 + 0.75$

$P_{25} = 21.75$

Solving (c): The 65th percentile

This is calculated as:

$P_{65} = 65 * \frac{N +1}{100}$

$P_{65} = 65 * \frac{8 +1}{100}$

$P_{65} = 65 * \frac{9}{100}$

$P_{65} = \frac{65 * 9}{100}$

$P_{65} = \frac{585}{100}$

$P_{65} = 5.85\th$

This is then calculated as:

$P_{65} = 5th + 0.85(6th - 5th)$

$P_{65} = 27 + 0.85(28 - 27)$

$P_{65} = 27 + 0.85(1)$

$P_{65} = 27 + 0.85$

$P_{65} = 27.85$

Solving (d): The 75th percentile

This is calculated as:

$P_{75} = 75 * \frac{N +1}{100}$

$P_{75} = 75 * \frac{8 +1}{100}$

$P_{75} = 75 * \frac{9}{100}$

$P_{75} = \frac{75 * 9}{100}$

$P_{75} = \frac{675}{100}$

$P_{75} = 6.75th$

This is then calculated as:

$P_{75} = 6th + 0.75(7th - 6th)$

$P_{75} = 28 + 0.75(30- 28)$

$P_{75} = 28 + 0.75(2)$

$P_{75} = 28 + 1.5$

$P_{75} = 29.5$

7 0

3 years ago

How many numbers are equal to the sum of two odd, one-digit numbers?

Dennis_Churaev [7]

Answer:

Seven numbers.

Step-by-step explanation:

Finding the numbers, which are equal to the sum of two odd number and it has to be single digit number.

Lets look into numbers which are odd and single digit.

1 = $1+3, 1+5, 1+7, 1+9$

∴ Sum of the number is $4,6,8\ and\ 10$

3 = $3+5, 3+7, 3+9$

∴ Sum of above number is $8,10\ and\ 12$

5 = $5+7, 5+9$

∴ Sum of above number is $12\ and\ 14$

7= $7+9$

∴ Sum of above number is $16$

Now, accumlating numbers which are fullfiling the criteria, however, making sure no number should get repeated.

∴ Numbers are: $4,6,8,10,12,14\ and\ 16$

Hence, there are total 7 numbers, which are equal to the sum of two odd, one-digit numbers.

4 0

3 years ago

Use the diagram to answer the question

koban [17]

Answer:

$m\angle EFG=52^{o}$

Step-by-step explanation:

We have been given that line m is parallel to line p, $m\angle HEF=39^{o}$ and $m\angle IGF=13^{o}$ .

Since line m is parallel to line p and EJ is a transversal, so measure of angle EJG will be 39 degrees as angle EJG is alternate interior angle of angle HEF. Both angles are inside parallel lines m and p and on opposite side of transversal EJ.

We can see that angle EFG is exterior angle of triangle GFJ. Since the measure of an exterior angle of a triangle equals to the sum of the opposite interior angles.

We can see that angle IGF and angle EJG are opposite interior angles of angle EFG.

$m\angle EFG=m\angle IGF+m\angle EJG$

Upon substituting our given values we will get,

$m\angle EFG=13^{o}+39^{o}$

$m\angle EFG=52^{o}$

Therefore, measure of angle EFG is 52 degrees.

3 0

3 years ago

Assessment items Eleni works out 15 fewer minutes on Tuesday than on Monday. She worked out 70 minutes on Tuesday. Use the five-

Kobotan [32]

Answer:

85 minutes.

Step-by-step explanation:

T = Tuesday

M = Monday

T = M - 15, 70 = M - 15, M = 85 minutes.

Since she worked out 15 minutes less than monday on tuesday, you add 15 to 70, since thats what she did on tuesday.

6 0

3 years ago

Write the equation in exponential form. log4 1/16 = -2

Allisa [31]

The answer is 4^-2 = 1/16

4 0

3 years ago