# 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 :)

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
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

1. 👍
2. 👎
3. ℹ️
4. 🚩
👤
oobleck
2. I don’t understand #2 and #5

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### math

Let f be the function with f(0) = 1/ (pi)^2, f(2) = 1/(pi)^2, and the derivative given by f'(x) = (x+1)cos ((pi)(x)). How many values of x in the open interval (0, 2) satisfy the conclusion of the Mean Value Theorem for the

2. ### Calculus

The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Right Rectangle Approximation, using the 4 intervals between those given

3. ### Calculus

1. The graph of f ′′(x) is continuous and decreasing with an x-intercept at x = –3. Which of the following statements must be true? A. The graph of f is always concave down. B. The graph of f has an inflection point at x =

4. ### Calculus

The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in the table below. Use the data in the table to approximate f '(3.5) x 3 4 7 10 13 f(x) 2 8 10 12 22

1. ### Calculus

A particle moves on the x-axis so that its position is continuous on the interval [3, 13] with some of its values for its velocity v(t) given in the table below. Use a right hand sum with 4 intervals to approximate the total

2. ### calculus

The function f is continuous on the closed interval [0,2] and has values that are given in the table below x = 0| 1 | 2 ____________ f(x) = 1| k | 2 The equation f(x) = 1/2 must have at least two solutions in the interval [0,2] if

3. ### Calculus

The function f is continuous on the interval [2, 10] with some of its values given in the table below. Use a trapezoidal approximation with 4 trapezoids to approximate of integral from 2 to 10 f(x)dx x 2 4 7 9 10 f(x) 0 3 8 15 18

4. ### calculus

The function f is continuous on the closed interval [0,6] and has values that are given in the table below. x |0|2|4|6 f(x)|4|K|8|12 The trapezoidal approximation for(the integral): 6 S f(x) dx 1 found with 3 subintervals of equal

1. ### Calculus

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 Trapezoidal Sum Approximation, using the intervals between those given points.

2. ### Statistics

State whether the data described below are discrete or continuous, and explain why. The number of pieces of mail a person receives each day. A. The data are discrete because the data can take on any value in an interval. B. The

3. ### Math

Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x) = 4x3 − 3x2, [−1, 2]

4. ### Calculus

f is a continuous function with a domain [−3, 9] such that f(x)= 3 , -3 ≤ x < 0 -x+3 , 0 ≤ x ≤ 6 -3 , 6 < x ≤ 9 and let g(x)= ∫ f(t) dt where a=-2 b=x On what interval is g increasing? Justify your answer. For 0 ≤ x