Calculus

1. The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the intervals between those given points.

x 10 12 15 19 20
f(x) –2 –5 –9 –12 –16
A. –9.250
B. –10.100
C. –7.550 <———— my choice
D. –6.700

2. The table of values below shows the rate of water consumption in gallons per hour at selected time intervals from t = 0 to t = 12.

Using a right Riemann sum with 5 subintervals estimate the total amount of water consumed in that time interval.

x 0 2 5 7 11 12
f(x) 5.7 5.0 2.0 1.2 0.6 0.4

A.2.742
B. 21.2
C. 32.9
D. None of these

3. The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in the table below. Find the average rate of change of f(x) over the interval [3, 13].

x 3 4 7 10 13
f(x) 2 8 10 12 22

4. f is a differentiable function on the interval [0, 1] and g(x) = f(3x). The table below gives values of f '(x). What is the value of g '(0.1)?

x 0.1 0.2 0.3 0.4 0.5
f '(x) 1 2 3 –4 5

A.1
B. 3
C. 9
D. Cannot be determined

5.
f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(3x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1).

x 1 2 3 4 5 6
f(x) 0 3 2 1 2 0
g(x) 1 3 2 6 5 0
f '(x) 3 2 1 4 0 2
g '(x) 1 5 4 3 2 0

Please help me! Oobleck, Thank so you so so much in advance and I greatly appreciate it!(I referred to you because most likely you’re usually the one who responds) so thank you again! I really appreciate all the help :)

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  1. #1.
    x 10 12 15 19 20
    f(x) –2 –5 –9 –12 –16
    Approximate the integral by
    -2*2 + -5*3 + -9*4 + -12*1 = -67
    Care to reconsider?

    #2. Just another sum problem.
    #3 avg rate of change is just (f(13)-f(3))/(13-3)
    #4. You already did one of these. g'(x) = f'(3x)*3
    #5. h'(1) = g'(f(3))*f'(1) - Review the chain rule stuff

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    oobleck
  2. I don’t understand #2 and #5

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