Use the guidelines of this section to sketch the curve. y = x ln x Data
Question:
Use the guidelines of this section to sketch the curve.
y = x – ln x
Data from section 4.5
Transcribed Image Text:
GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x) by hand. Not every item is relevant to every function. (For instance, a given curve might not have an asymptote or possess symmetry.) But the guidelines provide all the information you need to make a sketch that displays the most important aspects of the function. A. Domain It's often useful to start by determining the domain D of f, that is, the set of values of x for which f(x) is defined. B. Intercepts The y-intercept is f(0) and this tells us where the curve intersects the y-axis. To find the x-intercepts, we set y = 0 and solve for x. (You can omit this step if the equation is difficult to solve.) C. Symmetry (1) If f(-x) = f(x) for all x in D, that is, the equation of the curve is unchanged when x is replaced by -x, then f is an even function and the curve is symmetric about the y-axis. This means that our work is cut in half. If we know what the curve looks like for x > 0, then we need only reflect about the y-axis to obtain the complete curve [see Figure 3(a)]. Here are some examples: y = x²y = x¹, y = |x|, and y = cos x. (ii) If f(-x) = -f(x) for all x in D, then f is an odd function and the curve is symmetric about the origin. Again we can obtain the complete curve if we know what it looks like for x > 0. [Rotate 180° about the origin; see Figure 3(b).] Some simple examples of odd functions are y = x, y = x³, y = x³, and y = sin.x. (iii) If f(x + p) = f(x) for all x in D, where p is a positive constant, then f is called a periodic function and the smallest such number p is called the period. For instance, y = sin x has period 27 and y = tan x has period . If we know what the graph looks like in an interval of length p, then we can use translation to sketch the entire graph (see Figure 4).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (1 review)
The graph of ...View the full answer
Answered By
Nazrin Ziad
I am a post graduate in Zoology with specialization in Entomology.I also have a Bachelor degree in Education.I posess more than 10 years of teaching as well as tutoring experience.I have done a project on histopathological analysis on alcohol treated liver of Albino Mice.
I can deal with every field under Biology from basic to advanced level.I can also guide you for your project works related to biological subjects other than tutoring.You can also seek my help for cracking competitive exams with biology as one of the subjects.
3.30+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Solve each equation. Check the solutions. 14 x -= x - 5
-
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.
-
Use the guidelines of this section to sketch the curve. y= sin x/1 + cos x Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y...
-
Q-1. You are the new Governor of State Bank of Pakistan after Reza Baqir. For each of the situations listed below, decide if you would use Easy-Monetary policy or Tight-Monetary policy. a) RGDP...
-
Prepare a WBS for a spaghetti with meatballs dinner that includes a Caesar salad, a loaf of Italian bread, and wine. (Include the different components of the dinner at the upper level and the various...
-
1. Which vehicle is more "American"-a Chevrolet Silverado assembled in Mexico or a BMW made in South Carolina? Today, the typical motor vehicle sold in North America is made of components and...
-
The P\&ID reproduced in the next page shows an arrangement for the cooling of a hot effluent stream using cooling water. Unfortunately, the P\&ID includes a number of errors that could lead to...
-
Mackenzie Corp. is preparing the December 31, 2014, year-end financial statements. Following are selected unadjusted account balances: Estimated warranty liability ....... $ 6,460 Income tax...
-
Consider the following Java code: interface I { long f1(); long f2(); } abstract class C implements I { public long f1() { return 5; } } class C2 extends C { public long f1() { return 99; } public...
-
Use the guidelines of this section to sketch the curve. y = xe x2 Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x)...
-
Use the guidelines of this section to sketch the curve. y = ln(x 2 3x + 2) Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve...
-
Consider the half-reaction: If the ratio of concentrations of [MnO 4 ] : Mn 2+ is 100:1, determine E at pH values of (a) 0.5; (b) 2.0; (c) 3.5 (T = 298 K). Over this pH range, how does the ability...
-
Evaluate two of the following countries and address the following: Sustainability Measures and Environmental Regulation, Cost, Government Regulation, Intellectual Property, Reputation,...
-
Karen White is the sole owner of Crane Vista Park, a public camping ground near the Crater Lake National Recreation Area. Karen has compiled the following financial information as of December 31,...
-
In a warehouse of the Progressive Overnight Shipping Company, workers were hurrying to finish loading packages on Christmas Eve so they could finish early. Todd Meyers was carrying a large package,...
-
Given a set S of n unsorted, distinct real numbers and an integer k [2,n/2], your task here is to find the k-1 numbers $ < $ < < Sk-1 in S that partition the set S into k equal-sized subsets S2 (to...
-
The mechanics of accounting involve analyzing the effect on the accounting equation of financial transactions. Knowing how transactions affect the accounting equation allows you to consider and...
-
Describe how the variance and standard deviation are calculated and indicate how they are used as measures of risk.
-
we have to compute the letter grades for a course. The data is a collection of student records stored in a file. Each record consists of a name(up to 20 characters), ID (8 characters), the scores of...
-
Find an equation of the tangent line to the curve at the given point.1 3 V1 - 3, (-1, 2)
-
Trace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it. yA
-
Sketch the graph of a function f that is defined on R and continuous except for the stated discontinuities. Removable discontinuity at -2, infinite discontinuity at 2
-
Given the table T ID ColA ColB 10 20 30 40 50 60 70 80 90 and the table U ID ColC 10 100 10 110 40 120 What will the number returned from the query? select count(*) from T left outer join U on T.ID =...
-
In R, write code for the following a) uniform distribution on between 0 and 1 b) exponential distribution at a rate of 0.3 Submit code as a .txt file
-
1. Create a console application (core). In the console program's main function, write the C# code to do the following: Declare integer variable Y, double variables X and Z, and string S. Initialize X...
Study smarter with the SolutionInn App