12Suppose f(x)(a) The rectangles in the graph on the left illustrate a left endpoint upper sum for f(x) on the interval 4 < x < 6.and it is an ?The value of this left endpoint upper sum isA the area of the regionRightendpointenclosed by y = f(x), the x-axis, and the vertical lines x = 4 and æ = 6.Left endpointupper sum(b) The rectangles in the graph on the right illustrate a right endpoint lower sum for f(x) on the interval 4 < x < 6, and it is anlower sumThe value of this right endpoint lower sum isA the area of the regionenclosed by y = f(x), the x-axis, and the vertical lines x = 4 and x = 6.

Answered: 12 Suppose f(x) %3D (a) The rectangles…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3. ( interval (-2,6]. Here is the student's work: %3D A student used the Mean Value theorem on the function f(x) = |x - 1| on the (1) I calculated f(-2) = 3 and f(6) = 5. %3D (2) Then LO-[(-2) L(6)-f(-2) %3D %3D (3) By the Mean Value Theorem there is a number c in the interval (-2, 6] so that f'(c) = (The sentences have been numbered only to make it easier to refer to them.) For each sentence, explain why the student did that step. If there are any mistakes, tell the student what is incorrect about their work.
2. Rectangular box is inscribed in a sphere of radius 5in. (a) Set up a function of 2 variables that describe volume of the box as a function of two of its sides. (b) Among those boxes find the one with largest volume (c) Explain why is your result guaranteeing the largest volume,
The rectangles in the graph below illustrate a left endpoint upper sum for f(x) = 17 on the interval [2,6|. The value of this left endpoint upper sum is and this upper sum is an overestimate of + the area of the region enclosed by y = f(x), the x- axis, and the vertical lines x = 2 and x = 6. y 3. 2 1 2 3 4 7 Left endpoint upper sum for y = 17 on [2, 6] 17 on the interval [2, 6]. The rectangles in the graph below illustrate a right endpoint lower sum for f(x) and this lower sum is an underestimate of + the area of the region enclosed by y = f(x), the x- The value of this right endpoint lower sum is axis, and the vertical lines x = 2 and x = 6.
Using the following infromation please answer the questions in the image. Let F(x)=6x^2 - 4x^4 Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).
Figure 3 Figure 3 shows a circle of radius 4 containing a triangle OPQ. (a) Find an expression giving the area, A, of the triangle as a function of 0, for 0 <0<. (b) Find an expression for A valid for 0 < 0 < 27. [Hint: Don't forget area is always positive!] (e) Sketch a graph of A as a function of 0 for 0sos 27. Label intercepts and put units on the axes.
(a) By reading values from the given graph of f, use five rectangles to find a lower estimate and an upper estimate for the area under the given graph of f from x = 0 to x = 10. Lower estimate 2 Upper estimate a (b) Repeat part (a) with 10 rectangles in each case. Lower estimate 2 Upper estimate 2
remall. We couldn Product rule with tables You might need: Calculator • Let g be a function such that g(1) = -2 and g'(1) = 7. • Let h be the function h(x) = VT. F(2) = g(x) - h(z). Let F be a function defined as F'(1) = Show Calculator Stuck? Review related articles/videos or use a hint. Do 4
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Which interval of 0-values corresponds to the shaded region in the graph of r = f(0) = 2.1 – 0? On the graph, a = 2.1. 2- a (Give your answer as an interval in the form (*,*). Use the symbol o for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express numbers in decimal notation to one decimal place.) Find the area A of the region. (Use decimal notation. Give your answer to two decimal places.) A =
Sketch the graph and find the area of the region described below. f(x) = -7-√√x -10 -10 -5 14 10 y 5- -10 10 y 5- 4 -10 -10 x 5 X 5 X -10 -10 -5 -5 10 y 5- -10 10 y 5- 4 -10- X 5 X 10 10 Find the area of the region bounded below by the graph of f(x) and above by the x-axis from x = 0 to x = 9. 36 X square units
The graph below shows the velocity (in feet per second) of an experimental car for 0≤ t ≤ 24 seconds along with the rectangles used to estimate the distance traveled. (a) Do the rectangles represent a left- or right-hand sum? (b) Do the rectangles lead to an overestimate or an underestimate of the actual distance traveled? ---Select--- (c) Determine the value of At. At = (d) Determine the estimated distance traveled for the rectangles displayed below. velocity ft/sec 596 344 164 Estimated distance traveled is 56 20 ---Select--- 18 Units ---Select--- t seconds
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