Question 1

Write sigma notation of 4 - 9 + 16 - 25 +... + .

Accepted Answer

B

Question 2

Evaluate the sum  .

Accepted Answer

A

Question 3

Evaluate  .

Accepted Answer

C

Question 4

Evaluate the  .

Accepted Answer

The answer of Evaluate the  .
...

Question 5

Find and evaluate the sum  .

Accepted Answer

The answer of Find and evaluate the sum  .
...

Question 6

Evaluate  .

Accepted Answer

The answer of Evaluate  .
...

Question 7

Express the sum  +  +  +  +..... +  using sigma notation.

Accepted Answer

The answer of Express the sum  +  +...

Question 8

Simplify the expression  .

Accepted Answer

The answer of Simplify the expression  .
...

Question 9

Express the sum in the series  .

Accepted Answer

The answer of Express the sum in the series ...

Question 10

Evaluate the sum  Hint:  =  -  .

Accepted Answer

The answer of Evaluate the sum  Hint:  =...

Question 11

Evaluate the sum  .

Accepted Answer

The answer of Evaluate the sum  .
...

Question 12

Express the sum  as a polynomial function of n.

Accepted Answer

The answer of Express the sum  as a polynomial...

Question 13

Find an approximation for the area under the curve y = 1 -  and above the x-axis fromx = 0 to x = 1 using a sum of areas of four rectangles each having width 1/4 and (a) tops lying under the curve, or (b) tops lying above the curve. What does this tell you about the actual area under the curve?

Accepted Answer

The answer of Find an approximation for the area under...

Question 14

Given that the area under the curve y =  and above the x-axis from x = 0 to x = a > 0 is  square units, find the area under the same curve from x = -2 to x = 3.

Accepted Answer

The answer of Given that the area under the curve...

Question 15

Construct and simplify a sum approximating the area above the x-axis and under the curve y =  between x = 0 and x = 3 by using n rectangles having equal widths and tops lying under or on the curve. Find the actual area as a suitable limit.

Accepted Answer

The answer of Construct and simplify a sum approximating the...

Question 16

Construct and simplify a sum approximating the area above the x-axis and under the curvey =  between x = 0 and x = 3 by using n rectangles having equal widths and tops lying above or on the curve. Find the actual area as a suitable limit.

Accepted Answer

The answer of Construct and simplify a sum approximating the...

Question 17

Write the area under the curve y = cos x and above the interval [0,  $\pi$/2] on the x-axis as the limit of a sum of areas of n rectangles of equal widths. Have the upper-right corners of the rectangles lie on the curve.

Accepted Answer

The answer of Write the area under the curve y...

Question 18

Given that  =  , find the area under y =  and above the interval [0, a] on the x-axis (where a > 0 ) by interpreting the area as a limit of a suitable sum.

Accepted Answer

The answer of Given that  =  , find...

Question 19

The limit   represents the area of a certain region in the xy-plane. Describe the region.

Accepted Answer

The answer of The limit   represents the area...

Question 20

By interpreting it as the area of a region in the xy-plane, evaluate the limit  .

Accepted Answer

The answer of By interpreting it as the area of...

Quiz 6: Integration

Write sigma notation of 4 - 9 + 16 - 25 +... + .

Evaluate the sum .

Evaluate .

Evaluate the .

Find and evaluate the sum .

Evaluate .

Express the sum + + + +..... + using sigma notation.

Simplify the expression .

Express the sum in the series .

Evaluate the sum Hint: = - .

Evaluate the sum .

Express the sum as a polynomial function of n.

Find an approximation for the area under the curve y = 1 - and above the x-axis fromx = 0 to x = 1 using a sum of areas of four rectangles each having width 1/4 and (a) tops lying under the curve, or (b) tops lying above the curve. What does this tell you about the actual area under the curve?

Given that the area under the curve y = and above the x-axis from x = 0 to x = a > 0 is square units, find the area under the same curve from x = -2 to x = 3.

Construct and simplify a sum approximating the area above the x-axis and under the curve y = between x = 0 and x = 3 by using n rectangles having equal widths and tops lying under or on the curve. Find the actual area as a suitable limit.

Construct and simplify a sum approximating the area above the x-axis and under the curvey = between x = 0 and x = 3 by using n rectangles having equal widths and tops lying above or on the curve. Find the actual area as a suitable limit.

Write the area under the curve y = cos x and above the interval [0, $\pi$ /2] on the x-axis as the limit of a sum of areas of n rectangles of equal widths. Have the upper-right corners of the rectangles lie on the curve.

Given that = , find the area under y = and above the interval [0, a] on the x-axis (where a > 0 ) by interpreting the area as a limit of a suitable sum.

Quiz 6: Integration

Write sigma notation of 4 - 9 + 16 - 25 +... + .

Evaluate the sum .

Evaluate .

Evaluate the .

Find and evaluate the sum .

Evaluate .

Express the sum + + + +..... + using sigma notation.

Simplify the expression .

Express the sum in the series .

Evaluate the sum Hint: = - .

Evaluate the sum .

Express the sum as a polynomial function of n.

Find an approximation for the area under the curve y = 1 - and above the x-axis fromx = 0 to x = 1 using a sum of areas of four rectangles each having width 1/4 and (a) tops lying under the curve, or (b) tops lying above the curve. What does this tell you about the actual area under the curve?

Given that the area under the curve y = and above the x-axis from x = 0 to x = a > 0 is square units, find the area under the same curve from x = -2 to x = 3.

Construct and simplify a sum approximating the area above the x-axis and under the curve y = between x = 0 and x = 3 by using n rectangles having equal widths and tops lying under or on the curve. Find the actual area as a suitable limit.

Construct and simplify a sum approximating the area above the x-axis and under the curvey = between x = 0 and x = 3 by using n rectangles having equal widths and tops lying above or on the curve. Find the actual area as a suitable limit.

Write the area under the curve y = cos x and above the interval [0, π\piπ /2] on the x-axis as the limit of a sum of areas of n rectangles of equal widths. Have the upper-right corners of the rectangles lie on the curve.

Given that = , find the area under y = and above the interval [0, a] on the x-axis (where a > 0 ) by interpreting the area as a limit of a suitable sum.

The limit represents the area of a certain region in the xy-plane. Describe the region.

By interpreting it as the area of a region in the xy-plane, evaluate the limit .

Write the area under the curve y = cos x and above the interval [0, $\pi$ /2] on the x-axis as the limit of a sum of areas of n rectangles of equal widths. Have the upper-right corners of the rectangles lie on the curve.