CALCULUS: EARLY TANSCENDENTALS
9th Edition
ISBN: 9780357531273
Author: Stewart
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 13.1, Problem 19E
To determine
To draw: the curve using projections on three coordinate planes.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Find the following limit or state that it does not exist. Assume b is a fixed real number.
(x-b) 40 - 3x + 3b
lim
x-b
x-b
...
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(x-b) 40 -3x+3b
A. lim
x-b
x-b
B. The limit does not exist.
(Type an exact answer.)
x4 -289
Consider the function f(x) =
2
X-17
Complete parts a and b below.
a. Analyze lim f(x) and
lim f(x), and then identify the horizontal asymptotes.
x+x
X--∞
lim
4
X-289
2
X∞ X-17
X - 289
lim
=
2
...
X∞ X - 17
Identify the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.
A. The function has a horizontal asymptote at y =
B. The function has two horizontal asymptotes. The top asymptote is y =
and the bottom asymptote is y = ☐ .
C. The function has no horizontal asymptotes.
b. Find the vertical asymptotes. For each vertical asymptote x = a, evaluate lim f(x) and lim f(x). Select the correct choice and, if necessary, fill in the answer boxes to complete your choice.
e
Explain why lim
x²-2x-35
X-7
X-7
lim (x+5), and then evaluate lim
X-7
x² -2x-35
x-7
x-7
Choose the correct answer below.
A.
x²-2x-35
The limits lim
X-7
X-7
and lim (x+5) equal the same number when evaluated using
X-7
direct substitution.
B. Since each limit approaches 7, it follows that the limits are equal.
C.
The numerator of the expression
X-2x-35
X-7
simplifies to x + 5 for all x, so the limits are
equal.
D.
Since
x²-2x-35
X-7
= x + 5 whenever x 7, it follows that the two expressions evaluate to the
same number as x approaches 7.
Now evaluate the limit.
x²-2x-35
lim
X-7
X-7
= (Simplify your answer.)
Chapter 13 Solutions
CALCULUS: EARLY TANSCENDENTALS
Ch. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Find the limit. 3. limt0(e3ti+t2sin2tj+cos2tk)Ch. 13.1 - Find the limit. 4. limt1(t2-tt-1i+t+8j+sintlntk)Ch. 13.1 - Find the limit. 5. limt1+t21t2,tan-1t,1e2ttCh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10E
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Prob. 16ECh. 13.1 - Draw the projection of the curve onto the given...Ch. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Find a vector equation and parametric equations...Ch. 13.1 - Find a vector equation and parametric equations...Ch. 13.1 - Match the parametric equations with the graphs...Ch. 13.1 - Match the parametric equations with the graphs...Ch. 13.1 - Match the parametric equations with the graphs...Ch. 13.1 - Match the parametric equations with the graphs...Ch. 13.1 - Match the parametric equations with the graphs...Ch. 13.1 - Match the parametric equations with the graphs...Ch. 13.1 - Prob. 31ECh. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.1 - Prob. 35ECh. 13.1 - Show that the curve with parametric equations x =...Ch. 13.1 - Find three different surfaces that contain the...Ch. 13.1 - Find three different surfaces that contain the...Ch. 13.1 - Prob. 39ECh. 13.1 - At what points does the helix r(t) = sin t, cos t,...Ch. 13.1 - Graph the curve with parametric equations x = sin...Ch. 13.1 - Graph the curve with parametric equations x = (1 +...Ch. 13.1 - Prob. 48ECh. 13.1 - Show that the curve with parametric equations x =...Ch. 13.1 - Prob. 50ECh. 13.1 - Prob. 51ECh. 13.1 - Prob. 52ECh. 13.1 - Prob. 53ECh. 13.1 - Prob. 54ECh. 13.1 - Prob. 55ECh. 13.1 - Prob. 56ECh. 13.1 - Prob. 57ECh. 13.1 - Prob. 58ECh. 13.1 - Properties of Limits Suppose u and v are vector...Ch. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - (a) Sketch the plane curve with the given vector...Ch. 13.2 - Prob. 4ECh. 13.2 - (a) Sketch the plane curve with the given vector...Ch. 13.2 - (a) Sketch the plane curve with the given vector...Ch. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Find the derivative of the vector function. 9....Ch. 13.2 - Prob. 10ECh. 13.2 - Find the derivative of the vector function. 11....Ch. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Find the unit tangent vector T(t) at the given...Ch. 13.2 - Find the unit tangent vector T(t) at the given...Ch. 13.2 - Prob. 23ECh. 13.2 - Find the unit tangent vector T(t) at the given...Ch. 13.2 - Prob. 25ECh. 13.2 - Prob. 26ECh. 13.2 - Prob. 27ECh. 13.2 - Find parametric equations for the tangent line to...Ch. 13.2 - Find a vector equation for the tangent line to the...Ch. 13.2 - Find the point on the curve r(t) = 2 cos t, 2 sin...Ch. 13.2 - Find parametric equations tor the tangent line to...Ch. 13.2 - Find parametric equations tor the tangent line to...Ch. 13.2 - Find parametric equations tor the tangent line to...Ch. 13.2 - (a) Find the point of intersection of the tangent...Ch. 13.2 - Prob. 35ECh. 13.2 - At what point do the curves r1(t) = t, 1 t, 3 +...Ch. 13.2 - Evaluate the integral. 35. 02(ti-t3j+3t5k)dtCh. 13.2 - Evaluate the integral. 36. 14(2t3/2i+(t+1)tk)dtCh. 13.2 - Evaluate the integral. 37....Ch. 13.2 - Evaluate the integral. 38....Ch. 13.2 - Evaluate the integral. 39....Ch. 13.2 - Evaluate the integral. 40. (te2ti+t1-tj+11-t2k)dtCh. 13.2 - Find r(t) if r'(t) = 2t i + 3t2 j + t k and r(1) =...Ch. 13.2 - Find r(t) if r'(t) = t i + et j + tet k and r(0) =...Ch. 13.2 - Prove Formula 1 of Theorem 3.Ch. 13.2 - Prove Formula 3 of Theorem 3.Ch. 13.2 - Prob. 47ECh. 13.2 - Prob. 48ECh. 13.2 - If u(t) = sin t, cos t, t) and v(t) = t, cos t,...Ch. 13.2 - Prob. 50ECh. 13.2 - Prob. 51ECh. 13.2 - Prob. 52ECh. 13.2 - Prob. 53ECh. 13.2 - Prob. 54ECh. 13.2 - Show that if r is a vector function such that r''...Ch. 13.2 - Prob. 56ECh. 13.2 - Prob. 57ECh. 13.2 - Prob. 58ECh. 13.2 - Prob. 59ECh. 13.2 - Prob. 60ECh. 13.3 - (a) Use Equation 2 to compute the length of the...Ch. 13.3 - Prob. 2ECh. 13.3 - Find the length of the curve. 1. r(t) =t, 3 cos t,...Ch. 13.3 - Find the length of the curve. 2. r(t)=2t,t2,13t3,...Ch. 13.3 - Find the length of the curve. 3. r(t)=2ti+etj+etk,...Ch. 13.3 - Find the length of the curve. 4. r(t) =cos t i +...Ch. 13.3 - Find the length of the curve. 5. r(t) = i + t2 j +...Ch. 13.3 - Find the length of the curve. 6. r(t) = t2 i + 9t...Ch. 13.3 - Find the length of the curve correct to four...Ch. 13.3 - Find the length of the curve correct to four...Ch. 13.3 - Find the length of the curve correct to four...Ch. 13.3 - Graph the curve with parametric equations x = sin...Ch. 13.3 - Let C be the curve of intersection of the...Ch. 13.3 - Find, correct to four decimal places, the length...Ch. 13.3 - Prob. 15ECh. 13.3 - Prob. 16ECh. 13.3 - Suppose you start at the point (0, 0. 3) and move...Ch. 13.3 - Reparametrize the curve r(t)=(2t2+11)i+2tt2+1j...Ch. 13.3 - (a) Find the unit tangent and unit normal vectors...Ch. 13.3 - (a) Find the unit tangent and unit normal vectors...Ch. 13.3 - (a) Find the unit tangent and unit normal vectors...Ch. 13.3 - (a) Find the unit tangent and unit normal vectors...Ch. 13.3 - (a) Find the unit tangent and unit normal vectors...Ch. 13.3 - (a) Find the unit tangent and unit normal vectors...Ch. 13.3 - Use Theorem 10 to find the curvature. 21. r(t) =...Ch. 13.3 - Use Theorem 10 to find the curvature. 22. r(t) = t...Ch. 13.3 - Use Theorem 10 to find the curvature. 23....Ch. 13.3 - Prob. 28ECh. 13.3 - Find the curvature of r(t) = t, t2, t3 at the...Ch. 13.3 - Graph the curve with parametric equations x = cos...Ch. 13.3 - Use Formula 11 to find the curvature. 27. y = x4...Ch. 13.3 - To find: The curvature of y=tanx using Formula 11....Ch. 13.3 - Use Formula 11 to find the curvature. 27. y = x4...Ch. 13.3 - At what point does the curve have maximum...Ch. 13.3 - At what point does the curve have maximum...Ch. 13.3 - Find an equation of a parabola that has curvature...Ch. 13.3 - (a) Is the curvature of the curve C shown in the...Ch. 13.3 - Prob. 38ECh. 13.3 - Prob. 39ECh. 13.3 - Prob. 41ECh. 13.3 - Prob. 42ECh. 13.3 - Prob. 43ECh. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - Prob. 46ECh. 13.3 - Curvature of Plane Parametric Curves The curvature...Ch. 13.3 - Curvature of Plane Parametric Curves The curvature...Ch. 13.3 - Prob. 49ECh. 13.3 - Consider the curvature at x = 0 for each member of...Ch. 13.3 - Prob. 51ECh. 13.3 - Prob. 52ECh. 13.3 - Find equations of the normal plane and osculating...Ch. 13.3 - Find equations of the normal plane and osculating...Ch. 13.3 - Find equations of the osculating circles of the...Ch. 13.3 - Prob. 56ECh. 13.3 - At what point on the curve x = t3, y = 3t, z = t4...Ch. 13.3 - Find equations of the normal and osculating planes...Ch. 13.3 - Prob. 60ECh. 13.3 - Prob. 61ECh. 13.3 - Prob. 62ECh. 13.3 - Show that the curvature is related to the tangent...Ch. 13.3 - Prob. 64ECh. 13.3 - Prob. 65ECh. 13.3 - Prob. 66ECh. 13.3 - Use Formula 14 to find the torsion at the given...Ch. 13.3 - Prob. 68ECh. 13.3 - Prob. 69ECh. 13.3 - Prob. 70ECh. 13.3 - Prob. 71ECh. 13.3 - Frenet-Serret Formulas The following formulas,...Ch. 13.3 - Show that the circular helix r(t)=acost,asint,bt ,...Ch. 13.3 - Find the curvature and torsion of the curve x =...Ch. 13.3 - The DNA molecule has the shape of a double helix...Ch. 13.4 - The table gives coordinates of a particle moving...Ch. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13.4 - Find the velocity, acceleration, and speed of a...Ch. 13.4 - Prob. 9ECh. 13.4 - Prob. 10ECh. 13.4 - Find the velocity, acceleration, and speed of a...Ch. 13.4 - Find the velocity, acceleration, and speed of a...Ch. 13.4 - Find the velocity, acceleration, and speed of a...Ch. 13.4 - Find the velocity and position vectors of a...Ch. 13.4 - Find the velocity and position vectors of a...Ch. 13.4 - Find the velocity and position vectors of a...Ch. 13.4 - The position function of a particle is given by...Ch. 13.4 - What force is required so that a particle of mass...Ch. 13.4 - A force with magnitude 20 N acts directly upward...Ch. 13.4 - Show that if a particle moves with constant speed,...Ch. 13.4 - A projectile is fired with an initial speed of 200...Ch. 13.4 - Rework Exercise 23 if the projectile is fired from...Ch. 13.4 - A ball is thrown at an angle of 45 to the ground....Ch. 13.4 - A projectile is tired from a tank with initial...Ch. 13.4 - A rifle is fired with angle of elevation 36. What...Ch. 13.4 - Prob. 28ECh. 13.4 - A medieval city has the shape of a square and is...Ch. 13.4 - Show that a projectile reaches three-quarters of...Ch. 13.4 - A ball is thrown eastward into the air from the...Ch. 13.4 - A ball with mass 0.8 kg is thrown southward into...Ch. 13.4 - Another reasonable model for the water speed of...Ch. 13.4 - Prob. 35ECh. 13.4 - (a) If a particle moves along a straight line,...Ch. 13.4 - Prob. 37ECh. 13.4 - Prob. 38ECh. 13.4 - Find the tangential and normal components of the...Ch. 13.4 - Prob. 40ECh. 13.4 - Find the tangential and normal components of the...Ch. 13.4 - Prob. 42ECh. 13.4 - The position function of a spaceship is...Ch. 13.4 - A rocket burning its onboard fuel while moving...Ch. 13.4 - Prob. 1APCh. 13.4 - Prob. 3APCh. 13 - Prob. 1CCCh. 13 - Prob. 2CCCh. 13 - Prob. 3CCCh. 13 - Prob. 4CCCh. 13 - Prob. 5CCCh. 13 - (a) What is the definition of curvature? (b) Write...Ch. 13 - Prob. 7CCCh. 13 - Prob. 8CCCh. 13 - State Keplers Laws.Ch. 13 - Prob. 1TFQCh. 13 - Prob. 2TFQCh. 13 - Prob. 3TFQCh. 13 - Prob. 4TFQCh. 13 - Prob. 5TFQCh. 13 - Prob. 6TFQCh. 13 - Prob. 7TFQCh. 13 - Determine whether the statement is true or false....Ch. 13 - Determine whether the statement is true or false....Ch. 13 - Prob. 10TFQCh. 13 - Prob. 11TFQCh. 13 - Determine whether the statement is true or false....Ch. 13 - Determine whether the statement is true or false....Ch. 13 - Prob. 14TFQCh. 13 - Prob. 15TFQCh. 13 - (a) Sketch the curve with vector function r(t) = t...Ch. 13 - Let r(t) = 2-t, (et 1)/t, ln(t + 1). (a) Find the...Ch. 13 - Prob. 3ECh. 13 - Find parametric equations for the tangent line to...Ch. 13 - If r(t) = t2 i + t cos t j + sin t k, evaluate...Ch. 13 - Prob. 6ECh. 13 - Prob. 7ECh. 13 - Prob. 8ECh. 13 - The helix r1(t) = cos t i + sin t j + t k...Ch. 13 - Prob. 10ECh. 13 - For the curve given by r(t) = sin3 t, cos3 t, sin2...Ch. 13 - Find the curvature of the ellipse x = 3 cos t, y =...Ch. 13 - Find the curvature of the curve y = x4 at the...Ch. 13 - Find an equation of the osculating circle of the...Ch. 13 - Find an equation of the osculating plane of the...Ch. 13 - The figure shows the curve C traced by a particle...Ch. 13 - A particle moves with position function r(t) = t...Ch. 13 - Find the velocity, speed, and acceleration of a...Ch. 13 - A particle starts at the origin with initial...Ch. 13 - An athlete throws a shot at an angle of 45 to the...Ch. 13 - A projectile is launched with an initial speed of...Ch. 13 - Prob. 22ECh. 13 - Prob. 23ECh. 13 - PROBLEM PLUS FIGURE FOR PROBLEM 1 1. A particle P...Ch. 13 - A projectile is fired from the origin with angle...Ch. 13 - (a) A projectile it fired from the origin down an...Ch. 13 - A ball rolls off a table with a speed of 2 ft/s....Ch. 13 - Find the curvature of the curve with parametric...Ch. 13 - If a projectile is fired with angle of elevation ...Ch. 13 - A cable has radius r and length L and is wound...Ch. 13 - Prob. 9PP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- A function f is even if f(x) = f(x) for all x in the domain of f. If f is even, with lim f(x) = 4 and x-6+ lim f(x)=-3, find the following limits. X-6 a. lim f(x) b. +9-←x lim f(x) X-6 a. lim f(x)= +9-←x (Simplify your answer.) b. lim f(x)= X→-6 (Simplify your answer.) ...arrow_forwardEvaluate the following limit. lim X-X (10+19) Select the correct answer below and, if necessary, fill in the answer box within your choice. 10 A. lim 10+ = 2 ☐ (Type an integer or a simplified fraction.) X-∞ B. The limit does not exist.arrow_forwardFind the following limit or state that it does not exist. x² +x-20 lim x-4 x-4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim x²+x-20 x-4 (Type an exact answer.) x→4 B. The limit does not exist.arrow_forward
- Determine the intervals on which the following function is continuous. f(x) = x - 5x + 6 2 X-9 On what interval(s) is f continuous? (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)arrow_forwardFind the following limit or state that it does not exist. 2 3x² +7x+2 lim X-2 6x-8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. lim 3x²+7x+2 6x-8 (Simplify your answer.) X-2 B. The limit does not exist.arrow_forwardFind the following limit or state that it does not exist. X-2 lim x-2 5x+6 - 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. lim X-2 X-2 15x+6 = (Type an exact answer.) - 4 B. The limit does not exist.arrow_forward
- (a) Sketch the graph of a function that is not continuous at 1, but is defined at 1. (b) Sketch the graph of a function that is not continuous at 1, but has a limit at 1. (a) Which of the following graphs shows a function that is not continuous at 1, but is defined at 1. ○ A. Ay ✓ B. 5 X ✓ (b) Which of the following graphs shows a function that is not continuous at 1, but has a limit at 1. ○ A. B. X y 5- -5 5 ✓ ✓ 5 ☑ 5 X y ☑ LVarrow_forwardIf lim f(x)=L and lim f(x) = M, where L and M are finite real numbers, then what must be true about L x-a x-a+ and M in order for lim f(x) to exist? x-a Choose the correct answer below. A. L = M B. LMarrow_forwardDetermine the following limit, using ∞ or - ∞ when appropriate, or state that it does not exist. lim csc 0 Select the correct choice below, and fill in the answer box if necessary. lim csc 0 = ○ A. 0→⭑ B. The limit does not exist and is neither ∞ nor - ∞.arrow_forward
- Is the function f(x) continuous at x = 1? (x) 7 6 5 4 3 2 1 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -71 Select the correct answer below: The function f(x) is continuous at x = 1. The right limit does not equal the left limit. Therefore, the function is not continuous. The function f(x) is discontinuous at x = 1. We cannot tell if the function is continuous or discontinuous.arrow_forwardQuestion Is the function f(x) shown in the graph below continuous at x = -5? f(z) 7 6 5 4 2 1 0 -10 -6 -5 -4 1 0 2 3 5 7 10 -1 -2 -3 -4 -5 Select the correct answer below: The function f(x) is continuous. The right limit exists. Therefore, the function is continuous. The left limit exists. Therefore, the function is continuous. The function f(x) is discontinuous. We cannot tell if the function is continuous or discontinuous.arrow_forwardThe graph of f(x) is given below. Select all of the true statements about the continuity of f(x) at x = -1. 654 -2- -7-6-5-4- 2-1 1 2 5 6 7 02. Select all that apply: ☐ f(x) is not continuous at x = -1 because f(-1) is not defined. ☐ f(x) is not continuous at x = −1 because lim f(x) does not exist. x-1 ☐ f(x) is not continuous at x = −1 because lim ƒ(x) ‡ ƒ(−1). ☐ f(x) is continuous at x = -1 J-←台arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Cengage Learning