Approximations in calculus

f(x) = x³ - x
Use a linear approximation centered at x = 2 to find f(2.5).

• 10.5
• 11
• 11.5
• 12

f(x) = 3x²
Will linear approximations to f give values that are higher than or lower than the actual value?

• Higher
• Lower

Based on the table, use a left 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)

Find the right-hand Riemann Sum, with three sub-intervals indicated by the table.

• 28

• 16

• 34

• 21

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.2

If an increasing or decreasing function is concave up, a Trapezoidal approximation is which of the following:

• Underestimate
• Unable to Determine
• Overestimate
• Exact Solution

Using 5 subintervals, calculate the distance traveled using a left sum.

• 360
• 420
• 396
• 390

Use a trapezoidal sum with four intervals from the table to estimate the integral of 0 to 9 of V(t).

• 155/2

• 134/2

• 186/2

• 151/2

Tags

CCSS.HSS.ID.B.6A