1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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}

You might be interested in
Fritz benjamin buys a car costing $12300. He agrees to make payment at the end of each month period for 8 years. He pays 7.2% in
loris [4]
12300=X[((1-(1+(0.072/12)^(-12*8))/(0.072/12)]
Solve for x
X=168.92
4 0
3 years ago
The water park charges $3.00 per hour for parking and $2.50 for a 2-hour locker rental. Questions 1-8: Complete the tables by fi
valentinak56 [21]
The answer i choose is $5.50 because i added $3.00 and $2.50. so thats how i got my answer
3 0
3 years ago
Q10. Assertion: 2.05 Kg = 20500 g.
jeyben [28]

Answer:

b. only reason is correct

2.05 kg=2.05 ×1000 g

=2050 g

so the Assertion is incorrect

5 0
3 years ago
there are 320 seats in the airplane. passengers are taking 3/5 of the seats. There are 47 seats being used by flight attendants.
iogann1982 [59]

Answer: 124

Step-by-step explanation:

Multiply 320 by 3/5 (.6) and you will get 192. Then you subtract 320 by 47 and get 316. You subtract 192 from 316 and get 124.

8 0
3 years ago
I need help I will give 100 points and brainliest
Anit [1.1K]

Answer:

5. 9/2 6. 9/4 7. 7/2 8. 8/3 9. 2/3

Step-by-step explanation:

Hope I helped!!

4 0
3 years ago
Read 2 more answers
Other questions:
  • What is the missing number in the number sentence? (7 × 4) × 6 = 7 × ( __ × 6)
    6·1 answer
  • What’s the correct answer
    9·2 answers
  • Choose the equation below that represents the line that passes through the point (-2, -1) and has a slope of 5 ? A) y - 1 = 5(x
    11·2 answers
  • If the volume of the pyramid shown is 216 inches cubed, what is the area of its base? A rectangular pyramid with a height of 6 i
    7·1 answer
  • Show that tan (45°) = 1
    11·1 answer
  • Which expression can be used to find the area of triangle RTS?
    8·1 answer
  • Tylond puts $5,000 into a savings account that earns 4% simple interest. How much interest does he earn after
    6·1 answer
  • Help pls pls help pls
    8·1 answer
  • Help me pleaseee!!!!!
    11·1 answer
  • Learn with an example
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!