Topics 6.1-6.6 Review

A child is inflating a balloon by blowing air in to it. Each time he takes a breath, a small amount of air leaks out of the balloon. The table gives various values for time t (in seconds) and r'(t), the rate of change of the radius of the balloon in mm/sec. Use a Left Riemann Sum with three subintervals to approximate the total change in radius of the balloon on the interval [1,11].

• 14

• 16

• 27

• 38

A function g(x) has g'(x)>0 and g"(x)<0 on [1,5]. If a Right Riemann Sum is used to approximate the area between g(x) and the x-axis on the interval [1, 5], which of the following is correct?

Samantha is heating up some soup on the stove and various measurements of temperature, in degrees Celsius, are taken and given in the table above. Using a midpoint Riemann sum with three subintervals, which of the following expressions could be used to find the total degrees the soup accumulated over the interval [0,8]?

•  $\left[2\left(22\right)+2\left(35\right)+4\left(51\right)\right]$  

•  $\left[1\left(22\right)+3\left(35\right)+6\left(51\right)\right]$  

•  $\left[2\left(26\right)+2\left(48\right)+4\left(62\right)\right]$  

•  $\left[2\left(23\right)+2\left(37\right)+4\left(55\right)\right]$  

Which of the following limits is equal to

 $\int_1^3x^3dx$  

•  $\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(1+\frac{k}{n}\right)^3\frac{1}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(1+\frac{2k}{n}\right)^3\frac{2}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(1+\frac{k}{n}\right)^3\frac{2}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(1+\frac{2k}{n}\right)^3\frac{1}{n}$  

Gasoline is being pumped into a car. The rate that the gas is being pumped is given in the table at selected times. Use a right Riemann Sum with 3 equal subintervals to approximate the total gallons of gasoline pumped in the car over the 24 seconds.

• 8.72 gallons

• 9.92 gallons

• 6.96 gallons

• 7.51 gallons

Gasoline is being pumped into a car. The rate that the gas is being pumped is given in the table at selected times. Use a midpoint Riemann Sum with 3 equal subintervals to approximate the total gallons of gasoline pumped in the car over the 24 seconds.

• 8.72 gallons

• 9.92 gallons

• 6.96 gallons

• 7.51 gallons

Gasoline is being pumped into a car. The rate that the gas is being pumped is given in the table at selected times. Use a left Riemann Sum with 3 equal subintervals to approximate the total gallons of gasoline pumped in the car over the 24 seconds.

• 8.72 gallons

• 9.92 gallons

• 6.96 gallons

• 7.51 gallons

The rate that people are entering a local office is given in the table. Use a left Riemann sum with 4 subintervals to approximate the total number of people entering the office over the interval [0,7].

• 44 people

• 42 people

• 43 people

• 41 people

The rate that people are entering a local office is given in the table. Use a trapezoidal sum with 4 subintervals to approximate the total number of people entering the office over the interval [0,7].

• 44 people

• 42 people

• 43 people

• 41 people

Translate the definite integral into a Riemann sum.

 $\int_1^3\left(x+1\right)dx$  

•  $\lim_{n\rightarrow\infty}\sum_{k=1}^n\left[\left(1+\frac{2k}{n}\right)+1\right]\left(\frac{2}{n}\right)$  

•  $\lim_{n\rightarrow\infty}\sum_{k=1}^n\left[\left(2+\frac{k}{n}\right)+1\right]\left(\frac{1}{n}\right)$  

•  $\lim_{n\rightarrow\infty}\sum_{k=1}^n\left[\left(1+\frac{3k}{n}\right)+1\right]\left(\frac{3}{n}\right)$  

•  $\lim_{n\rightarrow\infty}\sum_{k=1}^n\left[\left(1+\frac{2k}{n}\right)+3\right]\left(\frac{2}{n}\right)$