 4.8.1: For Exercises 14, use the graphs of f and g to describethe motion o...
 4.8.2: For Exercises 14, use the graphs of f and g to describethe motion o...
 4.8.3: For Exercises 14, use the graphs of f and g to describethe motion o...
 4.8.4: For Exercises 14, use the graphs of f and g to describethe motion o...
 4.8.5: In Exercises 511, write a parameterization for the curves inthe xy...
 4.8.6: In Exercises 511, write a parameterization for the curves inthe xy...
 4.8.7: In Exercises 511, write a parameterization for the curves inthe xy...
 4.8.8: In Exercises 511, write a parameterization for the curves inthe xy...
 4.8.9: In Exercises 511, write a parameterization for the curves inthe xy...
 4.8.10: In Exercises 511, write a parameterization for the curves inthe xy...
 4.8.11: In Exercises 511, write a parameterization for the curves inthe xy...
 4.8.12: Exercises 1217 give parameterizations of the unit circle or apart o...
 4.8.13: Exercises 1217 give parameterizations of the unit circle or apart o...
 4.8.14: Exercises 1217 give parameterizations of the unit circle or apart o...
 4.8.15: Exercises 1217 give parameterizations of the unit circle or apart o...
 4.8.16: Exercises 1217 give parameterizations of the unit circle or apart o...
 4.8.17: Exercises 1217 give parameterizations of the unit circle or apart o...
 4.8.18: In Exercises 1820, what curves do the parametric equationstrace out...
 4.8.19: In Exercises 1820, what curves do the parametric equationstrace out...
 4.8.20: In Exercises 1820, what curves do the parametric equationstrace out...
 4.8.21: In Exercises 2126, the parametric equations describe the motionof a...
 4.8.22: In Exercises 2126, the parametric equations describe the motionof a...
 4.8.23: In Exercises 2126, the parametric equations describe the motionof a...
 4.8.24: In Exercises 2126, the parametric equations describe the motionof a...
 4.8.25: In Exercises 2126, the parametric equations describe the motionof a...
 4.8.26: In Exercises 2126, the parametric equations describe the motionof a...
 4.8.27: In Exercises 2729, find an equation of the tangent line to thecurve...
 4.8.28: In Exercises 2729, find an equation of the tangent line to thecurve...
 4.8.29: In Exercises 2729, find an equation of the tangent line to thecurve...
 4.8.30: For Exercises 3033, find the speed for the given motion of aparticl...
 4.8.31: For Exercises 3033, find the speed for the given motion of aparticl...
 4.8.32: For Exercises 3033, find the speed for the given motion of aparticl...
 4.8.33: For Exercises 3033, find the speed for the given motion of aparticl...
 4.8.34: Find parametric equations for the tangent line at t = 2for 30.
 4.8.35: 3536 show motion twice around a square, beginningat the origin at t...
 4.8.36: 3536 show motion twice around a square, beginningat the origin at t...
 4.8.37: A line is parameterized by x = 10 + t and y = 2t.(a) What part of t...
 4.8.38: A line is parameterized by x =2+3t and y =4+7t.(a) What part of the...
 4.8.39: (a) Explain how you know that the following two pairsof equations p...
 4.8.40: Describe the similarities and differences among the motionsin the p...
 4.8.41: What can you say about the values of a, b and k if theequationsx = ...
 4.8.42: Suppose a, b, c, d, m, n, p, q > 0. Match each pair ofparametric eq...
 4.8.43: Describe in words the curve represented by the parametricequationsx...
 4.8.44: (a) Sketch the parameterized curve x = t cos t, y =t sin t for 0 t ...
 4.8.45: The position of a particle at time t is given by x = et andy = 2e2t...
 4.8.46: For x and y in meters, the motion of the particle given byx = t3 3t...
 4.8.47: At time t, the position of a particle moving on a curve isgiven by ...
 4.8.48: Figure 4.111 shows the graph of a parameterized curvex = f(t), y = ...
 4.8.49: At time t, the position of a particle is x(t) = 5 sin(2t)and y(t) =...
 4.8.50: At time t, a projectile launched with angle of elevation and initia...
 4.8.51: Two particles move in the xyplane. At time t, the positionof parti...
 4.8.52: (a) Find d2y/dx2 for x = t3 + t, y = t2.(b) Is the curve concave up...
 4.8.53: (a) An object moves along the path x = 3t and y =cos(2t), where t i...
 4.8.54: The position of a particle at time t is given by x = et + 3and y = ...
 4.8.55: A particle moves in the xyplane so that its position attime t is g...
 4.8.56: Derive the general formula for the second derivatived2y/dx2 of a pa...
 4.8.57: Graph the Lissajous figures in 5760 using a calculator or computer....
 4.8.58: Graph the Lissajous figures in 5760 using a calculator or computer....
 4.8.59: Graph the Lissajous figures in 5760 using a calculator or computer....
 4.8.60: Graph the Lissajous figures in 5760 using a calculator or computer....
 4.8.61: A hypothetical moon orbits a planet which in turn orbitsa star. Sup...
 4.8.62: In 6263, explain what is wrong with the statement.The line segment ...
 4.8.63: In 6263, explain what is wrong with the statement.A circle of radiu...
 4.8.64: In 6465, give an example of:A parameterization of a quarter circle ...
 4.8.65: In 6465, give an example of:A parameterization of the line segment ...
 4.8.66: Are the statements in 6667 true of false? Give anexplanation for yo...
 4.8.67: Are the statements in 6667 true of false? Give anexplanation for yo...
Solutions for Chapter 4.8: PARAMETRIC EQUATIONS
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 4.8: PARAMETRIC EQUATIONS
Get Full SolutionsChapter 4.8: PARAMETRIC EQUATIONS includes 67 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Since 67 problems in chapter 4.8: PARAMETRIC EQUATIONS have been answered, more than 42291 students have viewed full stepbystep solutions from this chapter. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Cosecant
The function y = csc x

Extraneous solution
Any solution of the resulting equation that is not a solution of the original equation.

Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.

Horizontal line
y = b.

Imaginary axis
See Complex plane.

Inverse cosine function
The function y = cos1 x

Local extremum
A local maximum or a local minimum

Lower bound of f
Any number b for which b < ƒ(x) for all x in the domain of ƒ

Magnitude of a real number
See Absolute value of a real number

Pointslope form (of a line)
y  y1 = m1x  x 12.

Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

Standard form of a complex number
a + bi, where a and b are real numbers

Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.

Viewing window
The rectangular portion of the coordinate plane specified by the dimensions [Xmin, Xmax] by [Ymin, Ymax].

zcoordinate
The directed distance from the xyplane to a point in space, or the third number in an ordered triple.