Use the guidelines of this section to sketch the curve. y = e sin x Data from
Question:
Use the guidelines of this section to sketch the curve.
y = esin 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% (2 reviews)
The graph of ...View the full answer
Answered By
Chiranjib Thakur
I have no tutoring experience yet, but I can share my skills and knowledge gained from my education and work experiences. I have been a CPA since 2012 with 6 years of work experience in internal auditing and 4 years of work experience in accounting at the supervisory level.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
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...
-
Use the guidelines of this section to sketch the curve. y = 1/2 x sin x, 0 Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve...
-
a. Find the nth-order Taylor polynomials for the given function centered at the given point a, for n = 0, 1, and 2.b. Graph the Taylor polynomials and the function. f(x)=x, a = 9
-
Outline the ABC inventory control procedure. What is the purpose of classifying inventory items using this procedure?
-
Robertos Steakhouse tracks customer complaints every day and then follows up with their customers to resolve problems. For the past 30 days, they received a total of 22 complaints from unhappy...
-
Question: Sports Graphics, Inc. imports "Chill" brand coolers from Taiwan. Chill coolers have an outer shell of vinyl, with handles and pockets, and an inner layer of insulation. In a recent lawsuit,...
-
West Palm Company engaged in the following transactions involving promissory notes: May 3 Sold engines to Mittal Company for $120,000 in exchange for a 90-day, 12 percent promissory note. 16 Sold...
-
Bonita Wyatt is unable to reconcile the bank balance at January 31. Bonita's reconciliation is as follows. Cash balance per bank $3,800.20 Add: NSF check 570.00 Less: Bank service charge 30.00...
-
Find f. f"(x) = 24x 2 + 2x + 10. f(1) = 5, f'(1) = 3
-
Find f. f'(x) = 4/1 x 2 , f(1/2) = 1
-
Find parametrizations for the surfaces. The portion of the hemisphere x 2 + y 2 + z 2 = 10, y 0, in the first octant
-
S Ticketsales, Incorporated, receives $7,760,000 cash in advance ticket sales for a four-date tour of Bon Jovi. Record the advance ticket sales on October 31. Record the revenue earned for the first...
-
The loop track of a hot wheels car has a radius of curvature of 60 cm. Assume the loop is a perfect circle. A toy car weighs 50 grams, what is the minimum speed with which a car should enter the...
-
Two flat mirrors are perpendicular to each other. An incoming ray makes an angle of 8 = 35 with the first mirror as shown in the Figure. 02 03 0 a. [10 points] Find the value of the angle 03. b. [10...
-
A jeans maker is designing a new line of jeans called slams slam will sell for $ 3 7 0 per unit and cost $ 2 6 2 per unit and variable cost to make fix cost total is $ 6 4 , 5 0 0
-
What is your opinion on the following?: The question is: should Congress adopt the California Consumer Privacy Act (CCPA) as Federal law, and if so, what are the advantages and disadvantages of this...
-
At the beginning of 2016, JR Companys shareholders equity was as follows: Common stock, $5 par .........$35,000 Additional paid-in capital ....... 49,000 Retained earnings .......... 63,000 During...
-
Solve each problem. Find the coordinates of the points of intersection of the line y = 2 and the circle with center at (4, 5) and radius 4.
-
Express the number as a ratio of integers. 0.8 0.8888 . . .
-
Express the number as a ratio of integers. 10.135= 10.135353535 . . .
-
Express the number as a ratio of integers. 1.234567
-
The difference between net sales and cost of goods sold is called (a) gross profit. (b) net purchases. (c) goods available for sale. (d) the bottom line.
-
Soru 4 L-1 e-5s (s - 36) *s) A hibiri =? u(t-5)*[((e^(30-6t))/72) + ((e^(6t-30))/72) - 1/36] Cu(t-5)*[((e^(25-t))/34) + (2*(e^(t-5))/27) - 7/3] BCD Du(t-5)*[((e^(3-4t))/6) + ((e^(2t-3))/12) - 1/6] E...
-
Question 14 Isn convergent or divergent? convergent divergent Question 15 Why is the series in the previous problem convergent or divergent? Upload Choose a File Question 16 en Is convergent or...
Study smarter with the SolutionInn App