 10.3.1: In Exercises 14, find dy/dx.
 10.3.2: In Exercises 14, find dy/dx.
 10.3.3: In Exercises 14, find dy/dx.
 10.3.4: In Exercises 14, find dy/dx.
 10.3.5: In Exercises 514, find and and find the slope and concavity (if pos...
 10.3.6: In Exercises 514, find and and find the slope and concavity (if pos...
 10.3.7: In Exercises 514, find and and find the slope and concavity (if pos...
 10.3.8: In Exercises 514, find and and find the slope and concavity (if pos...
 10.3.9: In Exercises 514, find and and find the slope and concavity (if pos...
 10.3.10: In Exercises 514, find and and find the slope and concavity (if pos...
 10.3.11: In Exercises 514, find and and find the slope and concavity (if pos...
 10.3.12: In Exercises 514, find and and find the slope and concavity (if pos...
 10.3.13: In Exercises 514, find and and find the slope and concavity (if pos...
 10.3.14: In Exercises 514, find and and find the slope and concavity (if pos...
 10.3.15: In Exercises 15 and 16, find an equation of the tangent line at eac...
 10.3.16: In Exercises 15 and 16, find an equation of the tangent line at eac...
 10.3.17: In Exercises 1720, (a) use a graphing utility to graph the curve re...
 10.3.18: In Exercises 1720, (a) use a graphing utility to graph the curve re...
 10.3.19: In Exercises 1720, (a) use a graphing utility to graph the curve re...
 10.3.20: In Exercises 1720, (a) use a graphing utility to graph the curve re...
 10.3.21: In Exercises 2124, find the equations of the tangent lines at the p...
 10.3.22: In Exercises 2124, find the equations of the tangent lines at the p...
 10.3.23: In Exercises 2124, find the equations of the tangent lines at the p...
 10.3.24: In Exercises 2124, find the equations of the tangent lines at the p...
 10.3.25: In Exercises 25 and 26, find all points (if any) of horizontal and ...
 10.3.26: In Exercises 25 and 26, find all points (if any) of horizontal and ...
 10.3.27: In Exercises 2736, find all points (if any) of horizontal and verti...
 10.3.28: In Exercises 2736, find all points (if any) of horizontal and verti...
 10.3.29: In Exercises 2736, find all points (if any) of horizontal and verti...
 10.3.30: In Exercises 2736, find all points (if any) of horizontal and verti...
 10.3.31: In Exercises 2736, find all points (if any) of horizontal and verti...
 10.3.32: In Exercises 2736, find all points (if any) of horizontal and verti...
 10.3.33: In Exercises 2736, find all points (if any) of horizontal and verti...
 10.3.34: In Exercises 2736, find all points (if any) of horizontal and verti...
 10.3.35: In Exercises 2736, find all points (if any) of horizontal and verti...
 10.3.36: In Exercises 2736, find all points (if any) of horizontal and verti...
 10.3.37: In Exercises 3742, determine the t intervals on which the curve is ...
 10.3.38: In Exercises 3742, determine the t intervals on which the curve is ...
 10.3.39: In Exercises 3742, determine the t intervals on which the curve is ...
 10.3.40: In Exercises 3742, determine the t intervals on which the curve is ...
 10.3.41: In Exercises 3742, determine the t intervals on which the curve is ...
 10.3.42: In Exercises 3742, determine the t intervals on which the curve is ...
 10.3.43: Arc Length In Exercises 4346, write an integral that represents the...
 10.3.44: Arc Length In Exercises 4346, write an integral that represents the...
 10.3.45: Arc Length In Exercises 4346, write an integral that represents the...
 10.3.46: Arc Length In Exercises 4346, write an integral that represents the...
 10.3.47: Arc Length In Exercises 4752, find the arc length of the curve on t...
 10.3.48: Arc Length In Exercises 4752, find the arc length of the curve on t...
 10.3.49: Arc Length In Exercises 4752, find the arc length of the curve on t...
 10.3.50: Arc Length In Exercises 4752, find the arc length of the curve on t...
 10.3.51: Arc Length In Exercises 4752, find the arc length of the curve on t...
 10.3.52: Arc Length In Exercises 4752, find the arc length of the curve on t...
 10.3.53: Arc Length In Exercises 5356, find the arc length of the curve on t...
 10.3.54: Arc Length In Exercises 5356, find the arc length of the curve on t...
 10.3.55: Arc Length In Exercises 5356, find the arc length of the curve on t...
 10.3.56: Arc Length In Exercises 5356, find the arc length of the curve on t...
 10.3.57: Path of a Projectile The path of a projectile is modeled by the par...
 10.3.58: Path of a Projectile If the projectile in Exercise 57 is launched a...
 10.3.59: Folium of Descartes Consider the parametric equations and (a) Use a...
 10.3.60: Witch of Agnesi Consider the parametric equations and (a) Use a gra...
 10.3.61: Writing (a) Use a graphing utility to graph each set of parametric ...
 10.3.62: Writing (a) Each set of parametric equations represents the motion ...
 10.3.63: Surface Area In Exercises 6366, write an integral that represents t...
 10.3.64: Surface Area In Exercises 6366, write an integral that represents t...
 10.3.65: Surface Area In Exercises 6366, write an integral that represents t...
 10.3.66: Surface Area In Exercises 6366, write an integral that represents t...
 10.3.67: Surface Area In Exercises 6772, find the area of the surface genera...
 10.3.68: Surface Area In Exercises 6772, find the area of the surface genera...
 10.3.69: Surface Area In Exercises 6772, find the area of the surface genera...
 10.3.70: Surface Area In Exercises 6772, find the area of the surface genera...
 10.3.71: Surface Area In Exercises 6772, find the area of the surface genera...
 10.3.72: Surface Area In Exercises 6772, find the area of the surface genera...
 10.3.73: Give the parametric form of the derivative.
 10.3.74: Mentally determine (a) (b)
 10.3.75: Sketch a graph of a curve defined by the parametric equations and s...
 10.3.76: Sketch a graph of a curve defined by the parametric equations and s...
 10.3.77: Give the integral formula for arc length in parametric form.
 10.3.78: Give the integral formulas for the areas of the surfaces of revolut...
 10.3.79: Use integration by substitution to show that if is a continuous fun...
 10.3.80: Surface Area A portion of a sphere of radius is removed by cutting ...
 10.3.81: Area In Exercises 81 and 82, find the area of the region. (Use the ...
 10.3.82: Area In Exercises 81 and 82, find the area of the region. (Use the ...
 10.3.83: Areas of Simple Closed Curves In Exercises 8388, use a computer alg...
 10.3.84: Areas of Simple Closed Curves In Exercises 8388, use a computer alg...
 10.3.85: Areas of Simple Closed Curves In Exercises 8388, use a computer alg...
 10.3.86: Areas of Simple Closed Curves In Exercises 8388, use a computer alg...
 10.3.87: Areas of Simple Closed Curves In Exercises 8388, use a computer alg...
 10.3.88: Areas of Simple Closed Curves In Exercises 8388, use a computer alg...
 10.3.89: Centroid In Exercises 89 and 90, find the centroid of the region bo...
 10.3.90: Centroid In Exercises 89 and 90, find the centroid of the region bo...
 10.3.91: Volume In Exercises 91 and 92, find the volume of the solid formed ...
 10.3.92: Volume In Exercises 91 and 92, find the volume of the solid formed ...
 10.3.93: Cycloid Use the parametric equations and to answer the following. (...
 10.3.94: Use the parametric equations and to answer the following. (a) Use a...
 10.3.95: Involute of a Circle The involute of a circle is described by the e...
 10.3.96: Involute of a Circle The figure shows a piece of string tied to a c...
 10.3.97: (a) Use a graphing utility to graph the curve given by (b) Describe...
 10.3.98: Tractrix A person moves from the origin along the positive axis pul...
 10.3.99: True or False? In Exercises 99 and 100, determine whether the state...
 10.3.100: True or False? In Exercises 99 and 100, determine whether the state...
Solutions for Chapter 10.3: Parametric Equations and Calculus
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 10.3: Parametric Equations and Calculus
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus, edition: 8. Calculus was written by and is associated to the ISBN: 9780618502981. This expansive textbook survival guide covers the following chapters and their solutions. Since 100 problems in chapter 10.3: Parametric Equations and Calculus have been answered, more than 79107 students have viewed full stepbystep solutions from this chapter. Chapter 10.3: Parametric Equations and Calculus includes 100 full stepbystep solutions.

Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

Direction of an arrow
The angle the arrow makes with the positive xaxis

Equivalent arrows
Arrows that have the same magnitude and direction.

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Exponent
See nth power of a.

Graph of a function ƒ
The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.

Halflife
The amount of time required for half of a radioactive substance to decay.

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

Horizontal component
See Component form of a vector.

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Logarithmic function with base b
The inverse of the exponential function y = bx, denoted by y = logb x

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

Multiplicative inverse of a complex number
The reciprocal of a + bi, or 1 a + bi = a a2 + b2 ba2 + b2 i

Natural logarithm
A logarithm with base e.

Quadratic formula
The formula x = b 2b2  4ac2a used to solve ax 2 + bx + c = 0.

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Secant
The function y = sec x.

Statistic
A number that measures a quantitative variable for a sample from a population.

Xmin
The xvalue of the left side of the viewing window,.