 10.3.1: (a) To obtain dy/dx directly from the polar equationr = f( ), we ca...
 10.3.2: (a) What conditions on f(0) and f (0) guarantee that theline = 0 is...
 10.3.3: (a) To find the arc length L of the polar curve r = f( )( ), we can...
 10.3.4: The area of the region enclosed by a nonnegative polar curver = f( ...
 10.3.5: Find the area of the circle r = a by integration.
 10.3.6: 16 Find the slope of the tangent line to the polar curve for thegiv...
 10.3.7: 78 Calculate the slopes of the tangent lines indicated in theaccomp...
 10.3.8: 78 Calculate the slopes of the tangent lines indicated in theaccomp...
 10.3.9: 910 Find polar coordinates of all points at which the polarcurve ha...
 10.3.10: 910 Find polar coordinates of all points at which the polarcurve ha...
 10.3.11: 1112 Use a graphing utility to make a conjecture about thenumber of...
 10.3.12: 1112 Use a graphing utility to make a conjecture about thenumber of...
 10.3.13: 1318 Sketch the polar curve and find polar equations of thetangent ...
 10.3.14: 1318 Sketch the polar curve and find polar equations of thetangent ...
 10.3.15: 1318 Sketch the polar curve and find polar equations of thetangent ...
 10.3.16: 1318 Sketch the polar curve and find polar equations of thetangent ...
 10.3.17: 1318 Sketch the polar curve and find polar equations of thetangent ...
 10.3.18: 1318 Sketch the polar curve and find polar equations of thetangent ...
 10.3.19: 1922 Use Formula (3) to calculate the arc length of the polarcurve....
 10.3.20: 1922 Use Formula (3) to calculate the arc length of the polarcurve....
 10.3.21: 1922 Use Formula (3) to calculate the arc length of the polarcurve....
 10.3.22: 1922 Use Formula (3) to calculate the arc length of the polarcurve....
 10.3.23: (a) Show that the arc length of one petal of the roser = cos n is g...
 10.3.24: (a) Sketch the spiral r = e/8 (0 < +).(b) Find an improper integral...
 10.3.25: Write down, but do not evaluate, an integral for the area ofeach sh...
 10.3.26: Find the area of the shaded region in Exercise 25(d).
 10.3.27: In each part, find the area of the circle by integration.(a) r = 2a...
 10.3.28: (a) Show that r = 2 sin + 2 cos is a circle.(b) Find the area of th...
 10.3.29: 2934 Find the area of the region described. The region that is encl...
 10.3.30: 2934 Find the area of the region described. The region in the first...
 10.3.31: 2934 Find the area of the region described. The region enclosed by ...
 10.3.32: 2934 Find the area of the region described. The region enclosed by ...
 10.3.33: 2934 Find the area of the region described. The region enclosed by ...
 10.3.34: 2934 Find the area of the region described. The region swept out by...
 10.3.35: 3538 Find the area of the shaded region. 35
 10.3.36: 3538 Find the area of the shaded region. 36
 10.3.37: 3538 Find the area of the shaded region. 37
 10.3.38: 3538 Find the area of the shaded region. 38
 10.3.39: 3946 Find the area of the region described. The region inside the c...
 10.3.40: 3946 Find the area of the region described. The region outside the ...
 10.3.41: 3946 Find the area of the region described. The region inside the c...
 10.3.42: 3946 Find the area of the region described. The region that is comm...
 10.3.43: 3946 Find the area of the region described. The region between the ...
 10.3.44: 3946 Find the area of the region described. The region inside the c...
 10.3.45: 3946 Find the area of the region described. The region inside the c...
 10.3.46: 3946 Find the area of the region described. The region inside the c...
 10.3.47: 4750 TrueFalse Determine whether the statement is true orfalse. Exp...
 10.3.48: 4750 TrueFalse Determine whether the statement is true orfalse. Exp...
 10.3.49: 4750 TrueFalse Determine whether the statement is true orfalse. Exp...
 10.3.50: 4750 TrueFalse Determine whether the statement is true orfalse. Exp...
 10.3.51: (a) Find the error: The area that is inside the lemniscater2 = a2 c...
 10.3.52: Find the area inside the curve r2 = sin 2.
 10.3.53: A radial line is drawn from the origin to the spiralr = a(a > 0 and...
 10.3.54: As illustrated in the accompanying figure, suppose thata rod with o...
 10.3.55: (a) Show that the Folium of Descartes x3 3xy + y3 = 0can be express...
 10.3.56: (a) What is the area that is enclosed by one petal of the roser = a...
 10.3.57: One of the most famous problems in Greek antiquity wassquaring the ...
 10.3.58: Use a graphing utility to generate the polar graph of theequation r...
 10.3.59: Use a graphing utility to generate the graph of the bifoliumr = 2 c...
 10.3.60: Use Formula (9) of Section 10.1 to derive the arc lengthformula for...
 10.3.61: As illustrated in the accompanying figure, let P (r, ) be apoint on...
 10.3.62: 6263 Use the formula for obtained in Exercise 61. (a) Use the trigo...
 10.3.63: 6263 Use the formula for obtained in Exercise 61. Show that for a l...
 10.3.64: (a) In the discussion associated with Exercises 7580 ofSection 10.1...
 10.3.65: 6568 Sketch the surface, and use the formulas in Exercise 64to find...
 10.3.66: 6568 Sketch the surface, and use the formulas in Exercise 64to find...
 10.3.67: 6568 Sketch the surface, and use the formulas in Exercise 64to find...
 10.3.68: 6568 Sketch the surface, and use the formulas in Exercise 64to find...
 10.3.69: Writing(a) Show that if 0 1 < 2 and if r1 and r2 arepositive, then ...
 10.3.70: Writing In order to find the area of a region bounded bytwo polar c...
Solutions for Chapter 10.3: TANGENT LINES, ARC LENGTH, AND AREA FOR POLAR CURVES
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 10.3: TANGENT LINES, ARC LENGTH, AND AREA FOR POLAR CURVES
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 10.3: TANGENT LINES, ARC LENGTH, AND AREA FOR POLAR CURVES includes 70 full stepbystep solutions. Since 70 problems in chapter 10.3: TANGENT LINES, ARC LENGTH, AND AREA FOR POLAR CURVES have been answered, more than 42126 students have viewed full stepbystep solutions from this chapter.

Absolute minimum
A value ƒ(c) is an absolute minimum value of ƒ if ƒ(c) ? ƒ(x)for all x in the domain of ƒ.

Aphelion
The farthest point from the Sun in a planet’s orbit

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Compounded continuously
Interest compounded using the formula A = Pert

Constant
A letter or symbol that stands for a specific number,

Course
See Bearing.

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

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

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Right triangle
A triangle with a 90° angle.

Righthand limit of ƒ at x a
The limit of ƒ as x approaches a from the right.

Time plot
A line graph in which time is measured on the horizontal axis.