Question 1

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Accepted Answer

By Theorem 5.2, we have

$\sum\limits_{k=1}^{n} (3k^2 - k) = \frac{n(n+1)(6n+1)}{2}$

Substitute $n=25$ into the formula, we get:

$\sum\limits_{k=1}^{25} (3k^2 - k) = \frac{25	imes 26	imes 151}{2} = 10,471$

Therefore, the answer is choice B.

Question 2

Use the limit process to find the area of the region between the graph of the function  and x-axis over the interval  .

Accepted Answer

B

Question 3

Use the summation formulas to rewrite the expression  without the summation notation.

Accepted Answer

E

Question 4

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Accepted Answer

By expanding the summation using the properties of summation, we get:

∑(n^2 - 2n + 3) from n=1 to 10

= ∑n^2 from n=1 to 10 - 2∑n from n=1 to 10 + 3∑1 from n=1 to 10

= (1^2 + 2^2 + ... + 10^2) - 2(1 + 2 + ... + 10) + 3(10)

We can use Theorem 5.2, which states that:

∑n from n=1 to N = N(N+1)/2

∑n^2 from n=1 to N = N(N+1)(2N+1)/6

Plugging in N=10, we get:

∑n from n=1 to 10 = 10(10+1)/2 = 55

∑n^2 from n=1 to 10 = 10(10+1)(2(10)+1)/6 = 385

Plugging into our original expression, we get:

= (385) - 2(55) + 30 
= 300

Therefore, the answer is E: 66,033.

Question 5

Use left endpoints and 10 rectangles to find the approximation of the area of the region between the graph of the function  and the x-axis over the interval  . Round your answer to the nearest integer.

Accepted Answer

The answer of Use left endpoints and 10 rectangles to...

Question 6

The diagram below shows upper and lower sums for the function  using 4 subintervals. Use upper and lower sums to approximate the area of the region using the 4 subintervals.

Accepted Answer

The answer of The diagram below shows upper and lower...

Question 7

Find the limit of  as  .

Accepted Answer

The answer of Find the limit of  as ...

Question 8

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Accepted Answer

The answer of Use the properties of summation and Theorem...

Question 9

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Accepted Answer

The answer of Use the properties of summation and Theorem...

Question 10

Use left endpoints and 12 rectangles to find the approximation of the area of the region between the graph of the function  and the x-axis over the interval  . Round your answer to four decimal places.

Accepted Answer

The answer of Use left endpoints and 12 rectangles to...

Question 11

Find the sum given below.

Accepted Answer

The addition of the given hexadecimal numbers gives the result as 11eaa595_657b_be43_a696_0d102379d2c5_TB4584_11_TB4584_11.

Question 12

Use sigma notation to write the sum  .

Accepted Answer

The answer of Use sigma notation to write the sum...

Question 13

Find the limit of  as  .

Accepted Answer

The answer of Find the limit of  as ...

Question 14

Find the limit.

Accepted Answer

The answer of Find the limit. 
...

Question 15

Find the sum given below.

Accepted Answer

The answer of Find the sum given below. 
...

Question 16

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Accepted Answer

The answer of Use the properties of summation and Theorem...

Question 17

Find the sum given below.

Accepted Answer

The answer of Find the sum given below. 
...

Quiz 4: Section 2: Integration

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Use the limit process to find the area of the region between the graph of the function and x-axis over the interval .

Use the summation formulas to rewrite the expression without the summation notation.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Use left endpoints and 10 rectangles to find the approximation of the area of the region between the graph of the function and the x-axis over the interval . Round your answer to the nearest integer.

The diagram below shows upper and lower sums for the function using 4 subintervals. Use upper and lower sums to approximate the area of the region using the 4 subintervals.

Find the limit of as .

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Use left endpoints and 12 rectangles to find the approximation of the area of the region between the graph of the function and the x-axis over the interval . Round your answer to four decimal places.

Find the sum given below.

Use sigma notation to write the sum .

Find the limit of as .

Find the limit.

Find the sum given below.

Use the properties of summation and Theorem 5.2 to evaluate the sum.

Find the sum given below.