EP CALCULUS:EARLY TRANS.-MYLABMATH ACC.
3rd Edition
ISBN: 9780135873311
Author: Briggs
Publisher: PEARSON CO
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Textbook Question
Chapter 14.1, Problem 11E
Lines and line segments Find a function r(t) that describes the given line or line segment.
11. The line through P(3, 4, 5) that is orthogonal to the plane 2x − z = 4
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Find all solutions for v when v5 - 3q = 0.
How would i solve this. More info is that b =1 but it might be better to solve this before making the substitution
Let m(t) be a continuous function with a domain of all real numbers. The table below shows some of the values of m(t) .
Assume the characteristics of this function are represented in the table.
t
-3 -2 8 11
12
m(t) -7 6
3
-9
0
(a) The point (-3, -7) is on the graph of m(t). Find the corresponding point on the graph of the transformation y = -m(t) + 17.
(b) The point (8, 3) is on the graph of m(t). Find the corresponding point on the graph of the transformation y =
-m (−t) .
24
(c) Find f(12), if we know that f(t) = |m (t − 1)|
f(12) =
Chapter 14 Solutions
EP CALCULUS:EARLY TRANS.-MYLABMATH ACC.
Ch. 14.1 - Restrict the domain o f the vector function in...Ch. 14.1 - Explain why the curve in Example 5 lies on the...Ch. 14.1 - How many independent variables does the function...Ch. 14.1 - How many dependent scalar variables does the...Ch. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - How do you evaluate limtar(t), where r(t) = f(t),...Ch. 14.1 - How do you determine whether r(t) = f(t) i + g(t)...Ch. 14.1 - Find a function r(t) for the line passing through...Ch. 14.1 - Find a function r(t) whose graph is a circle of...
Ch. 14.1 - Prob. 9ECh. 14.1 - Prob. 10ECh. 14.1 - Lines and line segments Find a function r(t) that...Ch. 14.1 - 914. Lines and line segments Find a function r(t)...Ch. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Graphing curves Graph the curves described by the...Ch. 14.1 - Graphing curves Graph the curves described by the...Ch. 14.1 - Graphing curves Graph the curves described by the...Ch. 14.1 - Graphing curves Graph the curves described by the...Ch. 14.1 - Curves in space Graph the curves described by the...Ch. 14.1 - Curves in space Graph the curves described by the...Ch. 14.1 - Curves in space Graph the curves described by the...Ch. 14.1 - Curves in space Graph the curves described by the...Ch. 14.1 - Curves in space Graph the curves described by the...Ch. 14.1 - Curves in space Graph the curves described by the...Ch. 14.1 - Curves in space Graph the curves described by the...Ch. 14.1 - Curves in space Graph the curves described by the...Ch. 14.1 - Exotic curves Graph the curves described by the...Ch. 14.1 - Exotic curves Graph the curves described by the...Ch. 14.1 - Exotic curves Graph the curves described by the...Ch. 14.1 - Exotic curves Graph the curves described by the...Ch. 14.1 - Limits Evaluate the following limits. 41....Ch. 14.1 - Limits Evaluate the following limits. 42....Ch. 14.1 - Limits Evaluate the following limits. 43....Ch. 14.1 - Limits Evaluate the following limits. 44....Ch. 14.1 - Limits Evaluate the following limits. 45....Ch. 14.1 - Limits Evaluate the following limits. 46....Ch. 14.1 - Prob. 37ECh. 14.1 - Domains Find the domain of the following...Ch. 14.1 - Domains Find the domain of the following...Ch. 14.1 - Domains Find the domain of the following...Ch. 14.1 - Prob. 41ECh. 14.1 - Curve-plane intersections Find the points (if they...Ch. 14.1 - Curve-plane intersections Find the points (if they...Ch. 14.1 - Curve-plane intersections Find the points (if they...Ch. 14.1 - Matching functions with graphs Match functions af...Ch. 14.1 - Prob. 46ECh. 14.1 - 4750. Curve of intersection Find a function r(t)...Ch. 14.1 - 4750. Curve of intersection Find a function r(t)...Ch. 14.1 - 4750. Curve of intersection Find a function r(t)...Ch. 14.1 - Curve of intersection Find a function r(t) that...Ch. 14.1 - Golf slice A golfer launches a tee shot down a...Ch. 14.1 - Curves on surfaces Verify that the curve r(t) lies...Ch. 14.1 - 5256. Curves on surfaces Verify that the curve...Ch. 14.1 - Curves on surfaces Verify that the curve r(t) lies...Ch. 14.1 - Curves on surfaces Verify that the curve r(t) lies...Ch. 14.1 - 5256. Curves on surfaces Verify that the curve...Ch. 14.1 - 5758. Closest point on a curve Find the point P on...Ch. 14.1 - 5758. Closest point on a curve Find the point P on...Ch. 14.1 - Curves on spheres 75. Graph the curve...Ch. 14.1 - Prob. 60ECh. 14.1 - Prob. 61ECh. 14.1 - Closed plane curves Consider the curve r(t) = (a...Ch. 14.1 - Closed plane curves Consider the curve r(t) = (a...Ch. 14.1 - Closed plane curves Consider the curve r(t) = (a...Ch. 14.1 - Closed plane curves Consider the curve r(t) = (a...Ch. 14.1 - Limits of vector functions Let r(t) = (f(t), g(t),...Ch. 14.2 - Prob. 1QCCh. 14.2 - Suppose r(t) has units of m/s. Explain why T(t) =...Ch. 14.2 - Let u(t)=t,t,t and v(t)=1,1,1 compute...Ch. 14.2 - Let r(t)=1,2t,3t2. Compute r(t)dt.Ch. 14.2 - Prob. 1ECh. 14.2 - Explain the geometric meaning of r(t).Ch. 14.2 - Prob. 3ECh. 14.2 - Compute r(t) when r(t) = t10, 8t, cos t.Ch. 14.2 - How do you find the indefinite integral of r(t) =...Ch. 14.2 - How do you evaluate abr(t)dt?Ch. 14.2 - Find C if r(t)=et,3cost,t+10+C and r(0)=0,0,0.Ch. 14.2 - Find the unit tangent vector at t = 0 for the...Ch. 14.2 - Derivatives of vector-valued functions...Ch. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Derivatives of vector-valued functions...Ch. 14.2 - Prob. 13ECh. 14.2 - Derivatives of vector-valued functions...Ch. 14.2 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - Prob. 21ECh. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - Prob. 27ECh. 14.2 - Prob. 28ECh. 14.2 - Prob. 29ECh. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - Derivative rules Let...Ch. 14.2 - Derivative rules Let...Ch. 14.2 - Derivative rules Let...Ch. 14.2 - Derivative rules Let...Ch. 14.2 - Derivative rules Let...Ch. 14.2 - Derivative rules Let...Ch. 14.2 - Prob. 39ECh. 14.2 - Prob. 40ECh. 14.2 - Prob. 41ECh. 14.2 - Derivative rules Suppose u and v are...Ch. 14.2 - Derivative rules Let u(t) = 1, t, t2, v(t) = t2,...Ch. 14.2 - Prob. 44ECh. 14.2 - Derivative rules Let u(t) = 1, t, t2, v(t) = t2,...Ch. 14.2 - Prob. 46ECh. 14.2 - Derivative rules Let u(t) = 1, t, t2, v(t) = t2,...Ch. 14.2 - Derivative rules Let u(t) = 1, t, t2, v(t) = t2,...Ch. 14.2 - Derivative rules Compute the following...Ch. 14.2 - Derivative rules Compute the following...Ch. 14.2 - Derivative rules Compute the following...Ch. 14.2 - Derivative rules Compute the following...Ch. 14.2 - Higher-order derivatives Compute r(t) and r(t) for...Ch. 14.2 - Prob. 54ECh. 14.2 - Higher-order derivatives Compute r(t) and r(t) for...Ch. 14.2 - Higher-order derivatives Compute r(t) and r(t) for...Ch. 14.2 - Higher-order derivatives Compute r(t) and r(t) for...Ch. 14.2 - Higher-order derivatives Compute r(t) and r(t) for...Ch. 14.2 - Indefinite integrals Compute the indefinite...Ch. 14.2 - Prob. 60ECh. 14.2 - Indefinite integrals Compute the indefinite...Ch. 14.2 - Indefinite integrals Compute the indefinite...Ch. 14.2 - Indefinite integrals Compute the indefinite...Ch. 14.2 - Indefinite integrals Compute the indefinite...Ch. 14.2 - Finding r from r Find the function r that...Ch. 14.2 - Prob. 66ECh. 14.2 - Prob. 67ECh. 14.2 - Finding r from r Find the function r that...Ch. 14.2 - Finding r from r Find the function r that...Ch. 14.2 - Finding r from r Find the function r that...Ch. 14.2 - Definite integrals Evaluate the following definite...Ch. 14.2 - Definite integrals Evaluate the following definite...Ch. 14.2 - Definite integrals Evaluate the following definite...Ch. 14.2 - Definite integrals Evaluate the following definite...Ch. 14.2 - Definite integrals Evaluate the following definite...Ch. 14.2 - Definite integrals Evaluate the following definite...Ch. 14.2 - Definite integrals Evaluate the following definite...Ch. 14.2 - Definite integrals Evaluate the following definite...Ch. 14.2 - Prob. 79ECh. 14.2 - Prob. 80ECh. 14.2 - Prob. 81ECh. 14.2 - Prob. 82ECh. 14.2 - Prob. 83ECh. 14.2 - Relationship between r and r 78. Consider the...Ch. 14.2 - Relationship between r and r 79. Consider the...Ch. 14.2 - Prob. 86ECh. 14.2 - Relationship between r and r 81. Consider the...Ch. 14.2 - Relationship between r and r 82. Consider the...Ch. 14.2 - Relationship between r and r 83. Give two families...Ch. 14.2 - Motion on a sphere Prove that r describes a curve...Ch. 14.2 - Vectors r and r for lines a. If r(t) = at, bt, ct...Ch. 14.2 - Proof of Sum Rule By expressing u and v in terms...Ch. 14.2 - Proof of Product Rule By expressing u in terms of...Ch. 14.2 - Prob. 94ECh. 14.2 - Cusps and noncusps a. Graph the curve r(t) = t3,...Ch. 14.3 - Given r(t)=t,t2,t3, find v(t) and a(t).Ch. 14.3 - Find the functions that give the speed of the two...Ch. 14.3 - Prob. 3QCCh. 14.3 - Prob. 4QCCh. 14.3 - Prob. 5QCCh. 14.3 - Given the position function r of a moving object,...Ch. 14.3 - What is the relationship between the position and...Ch. 14.3 - Write Newtons Second Law of Motion in vector form.Ch. 14.3 - Write Newtons Second Law of Motion for...Ch. 14.3 - Given the acceleration of an object and its...Ch. 14.3 - Given the velocity of an object and its initial...Ch. 14.3 - The velocity of a moving object, for t 0, is...Ch. 14.3 - A baseball is hit 2 feet above home plate, and the...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Velocity and acceleration from position Consider...Ch. 14.3 - Comparing trajectories Consider the following...Ch. 14.3 - Comparing trajectories Consider the following...Ch. 14.3 - Comparing trajectories Consider the following...Ch. 14.3 - Comparing trajectories Consider the following...Ch. 14.3 - Comparing trajectories Consider the following...Ch. 14.3 - Comparing trajectories Consider the following...Ch. 14.3 - Prob. 27ECh. 14.3 - Carnival rides 28. Suppose the carnival ride in...Ch. 14.3 - Trajectories on circles and spheres Determine...Ch. 14.3 - Prob. 30ECh. 14.3 - Trajectories on circles and spheres Determine...Ch. 14.3 - Trajectories on circles and spheres Determine...Ch. 14.3 - Path on a sphere show that the following...Ch. 14.3 - Path on a sphere show that the following...Ch. 14.3 - Solving equations of motion Given an acceleration...Ch. 14.3 - Solving equations of motion Given an acceleration...Ch. 14.3 - Solving equations of motion Given an acceleration...Ch. 14.3 - Solving equations of motion Given an acceleration...Ch. 14.3 - Solving equations of motion Given an acceleration...Ch. 14.3 - Solving equations of motion Given an acceleration...Ch. 14.3 - Two-dimensional motion Consider the motion of the...Ch. 14.3 - Two-dimensional motion Consider the motion of the...Ch. 14.3 - Two-dimensional motion Consider the motion of the...Ch. 14.3 - Two-dimensional motion Consider the motion of the...Ch. 14.3 - Two-dimensional motion Consider the motion of the...Ch. 14.3 - Two-dimensional motion Consider the motion of the...Ch. 14.3 - Solving equations of motion Given an acceleration...Ch. 14.3 - Solving equations of motion Given an acceleration...Ch. 14.3 - Solving equations of motion Given an acceleration...Ch. 14.3 - Prob. 50ECh. 14.3 - Three-dimensional motion Consider the motion of...Ch. 14.3 - Three-dimensional motion Consider the motion of...Ch. 14.3 - Three-dimensional motion Consider the motion of...Ch. 14.3 - Three-dimensional motion Consider the motion of...Ch. 14.3 - Three-dimensional motion Consider the motion of...Ch. 14.3 - Prob. 56ECh. 14.3 - Prob. 57ECh. 14.3 - Trajectory properties Find the time of flight,...Ch. 14.3 - Trajectory properties Find the time of flight,...Ch. 14.3 - Trajectory properties Find the time of flight,...Ch. 14.3 - Trajectory properties Find the time of flight,...Ch. 14.3 - Motion on the moon The acceleration due to gravity...Ch. 14.3 - Firing angles A projectile is fired over...Ch. 14.3 - Prob. 64ECh. 14.3 - Speed on an ellipse An object moves along an...Ch. 14.3 - Golf shot A golfer stands 390 ft (130 yd)...Ch. 14.3 - Another golf shot A golfer stands 420 ft (140 yd)...Ch. 14.3 - Prob. 68ECh. 14.3 - Initial speed of a golf shot A golfer stands 420...Ch. 14.3 - Ski jump The lip of a ski jump is 8 m above the...Ch. 14.3 - Designing a baseball pitch A baseball leaves the...Ch. 14.3 - Parabolic trajectories Show that the...Ch. 14.3 - Prob. 73ECh. 14.3 - A race Two people travel from P(4, 0) to Q(4, 0)...Ch. 14.3 - Circular motion Consider an object moving along...Ch. 14.3 - Prob. 76ECh. 14.3 - A circular trajectory An object moves clockwise...Ch. 14.3 - Prob. 78ECh. 14.3 - Tilted ellipse Consider the curve r(t) = cos t,...Ch. 14.3 - Equal area property Consider the ellipse r(t) = a...Ch. 14.3 - Another property of constant | r | motion Suppose...Ch. 14.3 - Prob. 82ECh. 14.3 - Nonuniform straight-line motion Consider the...Ch. 14.4 - What does the arc length formula give for the...Ch. 14.4 - Consider the portion of a circle r(t) = (cos t,...Ch. 14.4 - Prob. 3QCCh. 14.4 - Find the length of the line given by r(t) = t, 2t,...Ch. 14.4 - Explain how to find the length of the curve r(t) =...Ch. 14.4 - Express the arc length of a curve in terms of the...Ch. 14.4 - Suppose an object moves in space with the position...Ch. 14.4 - An object moves on a trajectory given by r(t) = 10...Ch. 14.4 - Use calculus to find the length of the line...Ch. 14.4 - Explain what it means for a curve to be...Ch. 14.4 - Is the curve r(t) = cos t, sin t parameterized by...Ch. 14.4 - Arc length calculations Find the length of he...Ch. 14.4 - Arc length calculations Find the length of the...Ch. 14.4 - Arc length calculations Find the length of the...Ch. 14.4 - Arc length calculations Find the length of the...Ch. 14.4 - Prob. 13ECh. 14.4 - Arc length calculations Find the length of the...Ch. 14.4 - Arc length calculations Find the length of the...Ch. 14.4 - Prob. 16ECh. 14.4 - Arc length calculations Find the length of the...Ch. 14.4 - Arc length calculations Find the length of the...Ch. 14.4 - Arc length calculations Find the length of the...Ch. 14.4 - Arc length calculations Find the length of the...Ch. 14.4 - Arc length calculations Find the length of the...Ch. 14.4 - Arc length calculations Find the length of the...Ch. 14.4 - Speed and arc length For the following...Ch. 14.4 - Speed and arc length For the following...Ch. 14.4 - Speed and arc length For the following...Ch. 14.4 - Speed and arc length For the following...Ch. 14.4 - Speed of Earth Verify that the length of one orbit...Ch. 14.4 - Speed of Jupiter Verify that the length of one...Ch. 14.4 - Arc length approximations Use a calculator to...Ch. 14.4 - Prob. 30ECh. 14.4 - Arc length approximations Use a calculator to...Ch. 14.4 - Prob. 32ECh. 14.4 - Prob. 33ECh. 14.4 - Arc length parameterization Determine whether the...Ch. 14.4 - Arc length parameterization Determine whether the...Ch. 14.4 - Arc length parameterization Determine whether the...Ch. 14.4 - Prob. 37ECh. 14.4 - Prob. 38ECh. 14.4 - Prob. 39ECh. 14.4 - Arc length parameterization Determine whether the...Ch. 14.4 - Arc length parameterization Determine whether the...Ch. 14.4 - Arc length parameterization Determine whether the...Ch. 14.4 - Explain why or why not Determine whether the...Ch. 14.4 - Length of a line segment Consider the line segment...Ch. 14.4 - Tilted circles Let the curve C be described by...Ch. 14.4 - Prob. 46ECh. 14.4 - Prob. 47ECh. 14.4 - Toroidal magnetic field A circle of radius a that...Ch. 14.4 - Projectile trajectories A projectile (such as a...Ch. 14.4 - Variable speed on a circle Consider a particle...Ch. 14.4 - Arc length parameterization Prove that the line...Ch. 14.4 - Arc length parameterization Prove that the curve...Ch. 14.4 - Prob. 53ECh. 14.4 - Change of variables Consider the parameterized...Ch. 14.5 - What is the curvature of the circle r() =...Ch. 14.5 - Use the alternative curvature formula to compute...Ch. 14.5 - Prob. 3QCCh. 14.5 - Prob. 4QCCh. 14.5 - Prob. 5QCCh. 14.5 - Prob. 6QCCh. 14.5 - Prob. 7QCCh. 14.5 - What is the curvature of a straight line?Ch. 14.5 - Explain the meaning of the curvature of a curve....Ch. 14.5 - Give a practical formula for computing the...Ch. 14.5 - Interpret the principal unit normal vector of a...Ch. 14.5 - Give a practical formula for computing the...Ch. 14.5 - Explain how to decompose the acceleration vector...Ch. 14.5 - Explain how the vectors T, N, and B are related...Ch. 14.5 - How do you compute B?Ch. 14.5 - Give a geometrical interpretation of the torsion.Ch. 14.5 - How do you compute the torsion?Ch. 14.5 - Curvature Find the unit tangent vector T and the...Ch. 14.5 - Curvature Find the unit tangent vector T and the...Ch. 14.5 - Curvature Find the unit tangent vector T and the...Ch. 14.5 - Curvature Find the unit tangent vector T and the...Ch. 14.5 - Curvature Find the unit tangent vector T and the...Ch. 14.5 - Curvature Find the unit tangent vector T and the...Ch. 14.5 - Curvature Find the unit tangent vector T and the...Ch. 14.5 - Curvature Find the unit tangent vector T and the...Ch. 14.5 - Curvature Find the unit tangent vector T and the...Ch. 14.5 - Prob. 20ECh. 14.5 - Alternative curvature formula Use the alternative...Ch. 14.5 - Alternative curvature formula Use the alternative...Ch. 14.5 - Alternative curvature formula Use the alternative...Ch. 14.5 - Alternative curvature formula Use the alternative...Ch. 14.5 - Alternative curvature formula Use the alternative...Ch. 14.5 - Alternative curvature formula Use the alternative...Ch. 14.5 - Prob. 27ECh. 14.5 - Prob. 28ECh. 14.5 - Prob. 29ECh. 14.5 - Prob. 30ECh. 14.5 - Prob. 31ECh. 14.5 - Prob. 32ECh. 14.5 - Prob. 33ECh. 14.5 - Prob. 34ECh. 14.5 - Components of the acceleration Consider the...Ch. 14.5 - Components of the acceleration Consider the...Ch. 14.5 - Components of the acceleration Consider the...Ch. 14.5 - Components of the acceleration Consider the...Ch. 14.5 - Prob. 39ECh. 14.5 - Prob. 40ECh. 14.5 - Computing the binormal vector and torsion In...Ch. 14.5 - Computing the binormal vector and torsion In...Ch. 14.5 - Prob. 43ECh. 14.5 - Prob. 44ECh. 14.5 - Prob. 45ECh. 14.5 - Computing the binormal vector and torsion Use the...Ch. 14.5 - Computing the binormal vector and torsion Use the...Ch. 14.5 - Prob. 48ECh. 14.5 - Explain why or why not Determine whether the...Ch. 14.5 - Special formula: Curvature for y = f(x) Assume...Ch. 14.5 - Curvature for y = f(x) Use the result of Exercise...Ch. 14.5 - Prob. 52ECh. 14.5 - Prob. 53ECh. 14.5 - Curvature for y = f(x) Use the result of Exercise...Ch. 14.5 - Prob. 55ECh. 14.5 - Curvature for plane curves Use the result of...Ch. 14.5 - Curvature for plane curves Use the result of...Ch. 14.5 - Curvature for plane curves Use the result of...Ch. 14.5 - Curvature for plane curves Use the result of...Ch. 14.5 - Same paths, different velocity The position...Ch. 14.5 - Same paths, different velocity The position...Ch. 14.5 - Same paths, different velocity The position...Ch. 14.5 - Same paths, different velocity The position...Ch. 14.5 - Graphs of the curvature Consider the following...Ch. 14.5 - Graphs of the curvature Consider the following...Ch. 14.5 - Graphs of the curvature Consider the following...Ch. 14.5 - Graphs of the curvature Consider the following...Ch. 14.5 - Curvature of ln x Find the curvature of f(x) = ln...Ch. 14.5 - Curvature of ex Find the curvature of f(x) = ex...Ch. 14.5 - Prob. 70ECh. 14.5 - Finding radii of curvature Find the radius of...Ch. 14.5 - Finding radii of curvature Find the radius of...Ch. 14.5 - Finding radii of curvature Find the radius of...Ch. 14.5 - Designing a highway curve The function
r(t) =...Ch. 14.5 - Curvature of the sine curve The function f(x) =...Ch. 14.5 - Parabolic trajectory In Example 7 it was shown...Ch. 14.5 - Parabolic trajectory Consider the parabolic...Ch. 14.5 - Prob. 78ECh. 14.5 - Zero curvature Prove that the curve...Ch. 14.5 - Prob. 80ECh. 14.5 - Maximum curvature Consider the superparabolas...Ch. 14.5 - Alternative derivation of the curvature Derive the...Ch. 14.5 - Computational formula for B Use the result of part...Ch. 14.5 - Prob. 84ECh. 14.5 - Descartes four-circle solution Consider the four...Ch. 14 - Prob. 1RECh. 14 - Sets of points Describe the set of points...Ch. 14 - Graphing curves Sketch the curves described by the...Ch. 14 - Prob. 4RECh. 14 - Curves in space Sketch the curves described by the...Ch. 14 - Curves in space Sketch the curves described by the...Ch. 14 - Intersection curve A sphere S and a plane P...Ch. 14 - Vector-valued functions Find a function r(t) that...Ch. 14 - Vector-valued functions Find a function r(t) that...Ch. 14 - Vector-valued functions Find a function r(t) that...Ch. 14 - Vector-valued functions Find a function r(t) that...Ch. 14 - Vector-valued functions Find a function r(t) that...Ch. 14 - Prob. 13RECh. 14 - Intersection curve Find the curve r(t) where the...Ch. 14 - Intersection curve Find the curve r(t) where the...Ch. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RECh. 14 - Prob. 22RECh. 14 - Prob. 23RECh. 14 - Prob. 24RECh. 14 - Finding r from r Find the function r that...Ch. 14 - Finding r from r Find the function r that...Ch. 14 - Prob. 27RECh. 14 - Prob. 28RECh. 14 - Prob. 29RECh. 14 - Velocity and acceleration from position consider...Ch. 14 - Velocity and acceleration from position Consider...Ch. 14 - Solving equations of motion Given an acceleration...Ch. 14 - Prob. 33RECh. 14 - Orthogonal r and r Find all points on the ellipse...Ch. 14 - Modeling motion Consider the motion of the...Ch. 14 - Prob. 36RECh. 14 - Prob. 37RECh. 14 - Firing angles A projectile is fired over...Ch. 14 - Prob. 39RECh. 14 - Baseball motion A toddler on level ground throws a...Ch. 14 - Prob. 41RECh. 14 - Prob. 42RECh. 14 - Prob. 43RECh. 14 - Prob. 44RECh. 14 - Arc length Find the arc length of the following...Ch. 14 - Prob. 46RECh. 14 - Velocity and trajectory length The acceleration of...Ch. 14 - Prob. 48RECh. 14 - Arc length parameterization Find the description...Ch. 14 - Tangents and normals for an ellipse Consider the...Ch. 14 - Prob. 51RECh. 14 - Prob. 52RECh. 14 - Properties of space curves Do the following...Ch. 14 - Prob. 54RECh. 14 - Analyzing motion Consider the position vector of...Ch. 14 - Analyzing motion Consider the position vector of...Ch. 14 - Analyzing motion Consider the position vector of...Ch. 14 - Analyzing motion Consider the position vector of...Ch. 14 - Prob. 59RECh. 14 - Curve analysis Carry out the following steps for...Ch. 14 - Prob. 61RECh. 14 - Prob. 62RECh. 14 - Prob. 63RECh. 14 - Prob. 64RE
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- 3. Use the method of washers to find the volume of the solid that is obtained when the region between the graphs f(x) = √√2 and g(x) = secx over the interval ≤x≤ is rotated about the x-axis.arrow_forward4. Use cylindrical shells to find the volume of the solid generated when the region enclosed by the given curves is revolved about the x-axis. y = √√x, y = 0, y = √√3arrow_forward5 4 3 21 N -5-4-3-2 -1 -2 -3 -4 1 2 3 4 5 -5+ Write an equation for the function graphed above y =arrow_forward
- 6 5 4 3 2 1 -5 -4-3-2-1 1 5 6 -1 23 -2 -3 -4 -5 The graph above is a transformation of the function f(x) = |x| Write an equation for the function graphed above g(x) =arrow_forwardThe graph of y x² is shown on the grid. Graph y = = (x+3)² – 1. +10+ 69 8 7 5 4 9 432 6. 7 8 9 10 1 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 -2 -3 -4 -5 -6- Clear All Draw:arrow_forwardSketch a graph of f(x) = 2(x − 2)² − 3 4 3 2 1 5 ས་ -5 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 -5+ Clear All Draw:arrow_forward
- 5. Find the arc length of the curve y = 3x³/2 from x = 0 to x = 4.arrow_forward-6 -5 * 10 8 6 4 2 -2 -1 -2 1 2 3 4 5 6 -6 -8 -10- The function graphed above is: Concave up on the interval(s) Concave down on the interval(s) There is an inflection point at:arrow_forward6 5 4 3 2 1 -6 -5 -3 -2 3 -1 -2 -3 -4 -5 The graph above is a transformation of the function x² Write an equation for the function graphed above g(x) =arrow_forward
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