calculus sem2 re3view

What does this picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

Tags

CCSS.HSF.LE.B.5

For a function that is strictly decreasing, a right hand Riemann Sum is which of the following:

• Overestimate
• Underestimate
• Exact Solution
• Unable to Determine

Based on the table, use a Right Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

• 5(3) + 1(4) + 2(5) + 1(7)

• 5(4) + 1(5) + 2(7) + 1(6)

• 5(3) + 6(4) + 8(5) + 9(7)

• 0(3) + 5(4) + 6(5) + 8(7)

Use a midpoint Riemann Sum to approximate the area between 0 to 3 with 3 subintervals.

• 14

• 7

• 26

• 11

Find the area under the curve y =3x²-2x from x= 1 to x =5.

• 100
• 99
• 150
• 152

• Average Value
• Net Area
• Total Area
• Average Rate of Change

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

• Distance
• Displacement
• Velocity
• Acceleration

Velocity is different from speed because...

• Velocity is distance/time. Speed is displacement/time.

• Velocity is speed in a certain direction and can be positive or negative.

• Speed is velocity in a certain direction. Both can only be positive.

• Velocity is how much speed changes over time.

Given the differential equation dP/Dt=5P

A) Find the general solution for P to the differential equation

B)Find the particular solution for P to the differential equation given P(0)= 418

• A) P=Ce^5t

  B) P= 5e^418t

• A) P=Ce^5t

  B) P= 418e^5t

• A) P=Ce^t

  B) P= 418e^t

• A) P=Ce^10t

  B) P= 418e^10t

2. Solve the differential equation

𝑑𝑦/𝑑𝑡 =3𝑡²/𝑦 with initial condition

𝑦(2) = 0.

• 𝑦 = ln(15t)

• 𝑦 = 16t³

• 𝑦 = (2𝑡³ − 16)^1/2

• 𝑦 = (2𝑡³ −16)