Question: Let M(x) := ln|x| for x 0 and M(0) := 0. Show that M(x) = 1/x for all x 0. Explain why it

Let M(x) := ln|x| for x ≠ 0 and M(0) := 0. Show that Mʹ(x) = 1/x for all x ≠ 0. Explain why it does not follow that ∫2-2 (1/x)dx = ln|-2| - ln 2 = 0.

Step by Step Solution

★★★★★

3.44 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To conclude I can say that the func... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

829-C-F-M (479).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

Let X have an exponential distribution with = 1; that is, the pdf of X is f(x) = ex, 0

Q:

Let f(x) = ln x and let p n and q n be the nthorder Taylor polynomials for f centered at 1 and e, respectively. a. Find p 3 and q 3 . b. Graph f, p 3 , and q 3 on the interval [0, 4]. c. Complete the...

Q:

Let S be a nonempty subset of a linear space and let m dim cone S. For every x cone S, there exist x1,x2,...,xn S and α1, α2, . . ., αn + Such that x =...

Q:

Least Squares Approximation Hector D. Ceniceros 1 Least Squares Approximation Let f be a continuous function on [a, b]. We would like to find the best approximation to f by a polynomial of degree at...

Q:

Mohammed Yaaseen Gomdah E WeBWorK assignment due : 03/09/2016 at 03:00am EST. 1. (1 pt) Using disks or washers, nd the volume of the solid obtained by rotating the region bounded by the curves y =...

Q:

Can u just say if it's a b c or d 20-30 dthe.myschoolapp. What formula would be used to calculate the middle rectangle approximation of / (2x + 2)dx using five subintervals? 12.01 Semester Test:...

Q:

subscribers to an online fash 37. foll magazine. Due to competition from an 8-month-old competing magazine 38. The constant function g (x) = 5e" is an anti number C(t) of subscribers is expected to...

Q:

Need some help with problems 15 (uses figure 8.3) and 34(on the bottom of the page). Exercises 12-17 refer to the regions marked in Figure 8.3. Set up, but do not evaluate, an integral that...

Q:

868 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES 5. Let f (x, y) = 12x - yx2 + xy. (c) be ch (a) Show that the critical points (x, y) satisfy the equations max for t y(y - 2x + 1) =0, x ( 2y - x +...

Q:

868 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES 5. Let f (x, y) = 12x - yx2 +xy. (c) be c (a) Show that the critical points (x, y) satisfy the equations max for y(y - 2x + 1) = 0, x ( 2y - x+1)=0...

Q:

Research the Internet and write a report on intermodal shipping. Including its different forms, its technical aspects, its use around the world, some examples of companies that ace it, and the type...

Q:

Why do you think Michael Calderone had mixed feelings about using an offshore outsource company in the Philippines?

Q:

15.29 Refer to Exercise 15.28. In each case, specify the null and alternative hypotheses.

Q:

If we agree with the notion that products and services of today should not harm people of tomorrow, how would you redesign your favorite snack food to be more sustainable?

Q:

Use the rectangular coordinate system below each exercise to plot the three ordered pair solutions of the given equation. 1. 3x + y = 5; (1, 2), (0, 5), (2, -1) 2. y = -3x; (1, -3), (2, -6), ( -1, 3)...

Q:

Recall that the axes divide the plane into four quadrants as shown. For following Exercises if a and b are both positive numbers, determine whether each statement is true or false. 1. (-a, -b) lies...

Q:

Plot the points A(4, 3), B( -2, 3), C( -2, -1), and D(4, -1) on a rectangular coordinate system. 1. Find the length and the width of the figure. 2. Find the area of the figure.

Q:

Waste Industries is evaluating a $55,500 project with the following cash flows. Years Cash Flows 1 $ 9,120 2 20,200 3 26,600 4 16,300 5 26,300 The coefficient of variation for the project is .475....

Q:

Loan Amortization Problem Type your full name in the following order First Middle Last Number of letters in full name = Now assume that your annual salary = number of letters in your full name x...

Q:

Please assist me with the following problem. I'm having trouble filling in the statement of financial position. Any guidance appreciated. Required Information [The following information applies to...