Calculus Quiz 4/16/20

What formula is this?

• Intermediate Value Theorem

• Instantaneous Rate of Change

• Average Rate of Change

• Average Value of f

Based on the table, use a left hand 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)

The function f is continuous on the closed interval [0,6] and has values given in the table above. The trapezoidal approximation found with 3 subintervals is 52. What is the value of k?

• 2

• 6

• 7

• 10

The image displays the ______

• Limit definition of the first derivative

• Average Value of f

• Integral of f(a)

• Mean Value Theorem

If Distance is a function of Time, what is the average rate of change from 6 to 9 seconds?

• 3.3 feet per second
• -10 feet per second
• -3.3 feet per second
• 10 feet per second

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

when is the function f(x)=x²+6x+9 increasing?

• (3,∞)

• (-∞,3)

• (-3,-∞)

• (-3,∞)

Alec consumes beverages at a rate of r(x)=10 + 0.2x² beverages per hour, how many beverages does Alec drink in the first 16 hours?

• 25.068

• 433.067

• 5463.759

• 61.2

What is the average value of

f(x)= 6x² + 62x - 9 over (0,10)

• 5011

• 501.1

• 501

• 5010

Use the trapezoidal rule with n = 4 to estimate (to the nearest thousandth)  $\int_1^2\left(\frac{1}{1+x^3}\right)dx$  

• .257

• .514

• 2.056

• 1.028

Approximate the area using a Midpoint Riemann Sum on the interval [0,4] for  $f\left(x\right)=x^2+3$  

• 42

• 26

• 33

• 66