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lapo4ka [179]
3 years ago
10

(a) Use the definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit. lim n→∞ n i = 1 Correct

: Your answer is correct. (b) The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit in part (a). 13 + 23 + 33 + + n3 = n(n + 1) 2 2
Mathematics
1 answer:
Luba_88 [7]3 years ago
6 0

Splitting up the interval of integration into n subintervals gives the partition

\left[0,\dfrac1n\right],\left[\dfrac1n,\dfrac2n\right],\ldots,\left[\dfrac{n-1}n,1\right]

Each subinterval has length \dfrac{1-0}n=\dfrac1n. The right endpoints of each subinterval follow the sequence

r_i=\dfrac in

with i=1,2,3,\ldots,n. Then the left-endpoint Riemann sum that approximates the definite integral is

\displaystyle\sum_{i=1}^n\frac{{r_i}^3}n

and taking the limit as n\to\infty gives the area exactly. We have

\displaystyle\lim_{n\to\infty}\frac1n\sum_{i=1}^n\left(\frac in\right)^3=\lim_{n\to\infty}\frac{n^2(n+1)^2}{4n^3}=\boxed{\frac14}

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Ahhh please help i don’t understand thissss
gogolik [260]

Answer:

24y^3/x^5

Step-by-step explanation:

Since 6x and 4x are not in a parentheses, they are not being powered by anything. Therefore, those stay on the numerator side.

Anything to the power of something times another to the power of something is always added together. Since -1 + (-4) is -5, x would end up having a power of -5, which would just make it go on the denominator side with just a power of 5.

Same rule with y follows. This would make it 5+ (-2) = 3. Since this is a positive power, it stays at the numerator side.

5 0
3 years ago
Solve the absolute value equation or indicate that the equation has no solution. |x-5|=4
Lelu [443]

Step-by-step explanation:

bzjdfj7wirrididuwir9e8woao23893

3 0
1 year ago
All radical expressions that are equivalent to 3 2/5
SCORPION-xisa [38]

Answer:

15

Step-by-step explanation:

√15 (3√5)^2 3√5^2 3√10

4 0
3 years ago
Is the expression 5 (3m+2p) -4m equivalent to the expression 13p+11m-3p?
Aleksandr [31]
 5 (3m+2p) -4m= 15m +10p -4m
=11m +10p
--------------------------------------------------------
13p+11m-3p=10p -11m
-----------------------------------------------------------
Yes, 5 (3m+2p) -4m is  equivalent to the expression 13p+11m-3p as i worked out for you.. Hope this helps you!!! =')

7 0
3 years ago
Read 2 more answers
WITH PICTURE!!3. What is the value of x in the regular polygon below? (3 points)
monitta

Answer: FIRST OPTION.

Step-by-step explanation:

Regular polygons are those polygons whose sides are equal in length and whose angles are all equal.

By definition each interior angle of a Regular polygon,is:

\frac{180 ( n -2 )}{n}  (In degrees)

Where "n" is the number of sides of the polygon.

Observe the Regular polygon given in the exercise.

Since it has 6 sides, you can conclude that it is an Hexagon. Then:

n=6

Substituting into  \frac{180 ( n -2 )}{n}  and evaluating, you get:

\frac{180 ( 6 -2 )}{6}=120\°

Knowing this, you can write the following equation:

3x=120

Finally, you must solve for "x" in order to find its value. This is:

x=\frac{120}{3}\\\\x=40

8 0
3 years ago
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