Ask question

Ask question

All categories

1 year ago

13

Please help my assignment

1 answer:

m_a_m_a [10]1 year ago

3 0

There is no solution since ln(0) is undefined

You might be interested in

Find a formula for the sum of n terms. Use the formula to find the limit as n → [infinity]. lim n → [infinity] n 2 + i n 8 n i =

Masteriza [31]

Complete Question

Find a formula for the sum of n terms. $\sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )$

Use the formula to find the limit as $n \to \infty$

Answer:

$K_n = \frac{n + 73 }{n}$

$\lim_{n \to \infty} K_n = 1$

Step-by-step explanation:

So let assume that

$K_n = \sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )$

=> $K_n = \sum\limits_{i=1}^n ( \frac{16}{n} + \frac{2i}{n^2} )$

=> $K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)$

Generally

$\sum\limits_{i=1}^n (k) = \frac{1}{2} n (n + 1)$

So

$\sum\limits_{i=1}^n (8) = \frac{1}{2} * 8* (8 + 1)$

$\sum\limits_{i=1}^n (8) = 36$

$K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)$

and

$\sum\limits_{i=1}^n (i) = \frac{1}{2} n (n + 1)$

Therefore

$K_n = \frac{72}{n} + \frac{2}{n^2} * \frac{1}{2} n (n + 1 )$

$K_n = \frac{72}{n} + \frac{1}{n} (n + 1 )$

$K_n = \frac{72}{n} + 1 + \frac{1}{n}$

$K_n = \frac{72 + 1 + n }{n}$

$K_n = \frac{n + 73 }{n}$

Now $\lim_{n \to \infty} K_n = \lim_{n \to \infty} [\frac{n + 73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [\frac{n}{n} + \frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 + \frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 ] + \lim_{n \to \infty} [\frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = 1 + 0$

Therefore

$\lim_{n \to \infty} K_n = 1$

5 0

3 years ago

PLEASE ANSWER IN THE NEXT FIVE MINUTES!!! What is the volume of a rectangular prism with a height of 5 meters and a base with ar

cluponka [151]

Answer:

95 m³

Step-by-step explanation:

The volume (V) of a rectangular prism is

V = area of base × height

here area = 19 and h = 5, hence

V = 19 × 5 = 95 m³

3 0

3 years ago

Compare Loan Terms

zmey [24]

Answer:

Step-by-step explanation:

the answer is basically 4.5% and the 6%

5 0

2 years ago

Read 2 more answers

Find the rate of change for the function of change from x=-3 to x=1

Luba_88 [7]

Answer:

She's, "HOT"!

Step-by-step explanation:

8 0

2 years ago

Use a unit circle, a 30 degrees - 60 degrees - 90 degrees triangle, and an inverse function to find the degree measure of the

PolarNik [594]

150 is the answer I don’t think it is right

8 0

3 years ago