Concept explainers
To graph: The equations
Explanation of Solution
Given information:
The equations
Graph:
The graph of the equation
0 | |
2 | |
4 |
The graph of equation is provided below,
The graph of the equation
0 | |
2 | |
The graph of equation is provided below,
The graph of both equations in same figure is provided below,
From the graph it looks as the graphs intersect near the
Since, the graphs intersect each other at 2 points.
Thus, the graphs intersect in the given viewing rectangle. There are 2 intersection points.
Interpretation:
The graph of an equation in a viewing screen is a viewing rectangle.
The
The
Then, the display portion of the graph lies in the rectangle
The equations
Chapter 1 Solutions
Precalculus - A Custom Text for UNLV
- #IN A [2 pts.] C 0 II. Consider the circle C r = 4 cos 0 and the line Cr=sec as in the figure on the right. Let A and B be the points of intersection of the two curves as shown. 1. Find the polar coordinates of A and B. 2. Find a Cartesian equation of the tangent line to C at the point where [4 pts.] 3. Set up (and do not evaluate) a definite integral or a sum of definite integrals that yields the follow- ing: a. the length of the portion of C traced counterclockwise from A to B. b. the area of the shaded region. [2 pts.] [3 pts.] B Carrow_forwardI. Perform the following integrations. 1. L' (2x + 1)e³r da cot³ (ln x) csc³ (ln x) 2. dx х 3. 4. x² √1-92 dx 3x3 +14x+7 x² (x²+7) dxarrow_forwardIV. Consider the equation : y + z = 2. 1. Sketch a portion of the graph of π in the first octant in R3. Indicate proper rulings. [2 pts.] 2. Find an equation of the surface generated by revolving the trace of π on the the yz-plane about the y-axis. Sketch the surface of revolution. [3 pts.]arrow_forward
- IV. Consider the function f(x) = esin 2x 1. Find the second-degree Maclaurin polynomial of f(x). 2. Approximate esin 0.02 using the result in IV.1. Express your answer in decimal form.arrow_forwardIII. Find the center-radius form of the equation of the sphere having the line segment with endpoints P(1,-2, 1) and Q(5, 0, 1) as a diameter. [2.5 pts.]arrow_forwardII. Determine if the improper integral is convergent or divergent. 0 2x2 L dx -2 x3+8arrow_forward
- 2+5n2 1. Determine whether the sequence (b) converges or diverges. 2. Determine whether the following series converge or diverge. State the test you us 3n² - n I. Let bn = for n N with n ≥ 1. نے n=1 8 b. (bn)" n=1arrow_forwardII. Determine whether the following series converge or diverge. State the test you used. (4/2/3 po 1 1. n(Inn)2 n=3 2. 8 IM n=1 5" + sin² n 3n 00 1.3 " 3. (2n − 1) (n + 2)! - n=1arrow_forward7. Consider the following parametric curve: x = sint, y = 2 cost, for 0 ≤t≤ a) Eliminate the parameter to find a rectangular equation for the curve. b) Use the parametric equations to find the slope of the tangent line when t = c) Use the parametric equations to set up an integral to represent the arc length of the curve. You do not need to evaluate the integral.arrow_forward
- 10. Consider the polar equation r = sin² (2) a) Find the (rectangular) equation of the tangent line when 0 => b) Set up an integral to represent the arc length of the curve for 0arrow_forward2. Which of the following differential equations has the direction field shown? Explain your answer and support it with calculations. Full credit will not be given without sufficient justification. a) y' = x + 2y 31 12 b) y' = y - ¹× c) y' = (x + 1)(y+1) / 1 +-2 1-311 Harrow_forward8. Graph the polar equation r = 4 cos 30. Show work to fully justify your graph. 2 2 2 2arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning