 87.Q1: Differentiate: f(x) = 5x3 7x2 + 4x 11
 87.Q2: Differentiate: g(x) = (4x 9)3
 87.Q3: Differentiate: h(x) = sin3 x
 87.Q4: Differentiate: u(x) = sec 3x
 87.Q5: Differentiate: v(x) = e
 87.Q6: Differentiate: r(x) = 1/x
 87.Q7: Integrate: (1/x) dx
 87.Q8: Integrate: x dx
 87.Q9: Integrate: 3 dx
 87.Q10: Integrate: dx
 87.1: . Figure 87f shows the polar graph of the circle r = 10 sin , with...
 87.2: Find the length of the circle r = 10 sin in Figure 87f that is tra...
 87.3: For 310, a. Plot the graph, thus confirming the one given here. b. ...
 87.4: For 310, a. Plot the graph, thus confirming the one given here. b. ...
 87.5: For 310, a. Plot the graph, thus confirming the one given here. b. ...
 87.6: For 310, a. Plot the graph, thus confirming the one given here. b. ...
 87.7: For 310, a. Plot the graph, thus confirming the one given here. b. ...
 87.8: For 310, a. Plot the graph, thus confirming the one given here. b. ...
 87.9: For 310, a. Plot the graph, thus confirming the one given here. b. ...
 87.10: For 310, a. Plot the graph, thus confirming the one given here. b. ...
 87.11: Figure 87g shows the lemniscate of Bernoulli with polar equation W...
 87.12: The polar graph of r = csc + 4 is a conchoid of Nicomedes. The grap...
 87.13: Figure 87h shows these polar graphs. Cardioid: r = 4 + 4 cos Circl...
 87.14: Find the area of the region that is inside the circle r = 5 and out...
 87.15: Figure 87i shows the Archimedean spiral r = 0.5 . Figure 87i a. F...
 87.16: For the limaon r = 4 + 6 cos , find the area of the region that lie...
 87.17: Column Scroll Problem: The spiral design at the top of Ionic column...
 87.18: Line Problem: Show that the graph of r = sec is a line. Find the le...
 87.19: LP Record Project: In this project you will calculate the length of...
 87.20: Keplers Law Project: Figure 87j shows the path of a satellite in a...
 87.21: The Derivative dy/dx for Polar Coordinates Problem: Figure 87k sho...
 87.22: ProjectThe Angle Between the Radius and the Tangent Line: A remarka...
Solutions for Chapter 87: Lengths and Areas for Polar Coordinates
Full solutions for Calculus: Concepts and Applications  2nd Edition
ISBN: 9781559536547
Solutions for Chapter 87: Lengths and Areas for Polar Coordinates
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 32 problems in chapter 87: Lengths and Areas for Polar Coordinates have been answered, more than 19344 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Concepts and Applications, edition: 2. Calculus: Concepts and Applications was written by and is associated to the ISBN: 9781559536547. Chapter 87: Lengths and Areas for Polar Coordinates includes 32 full stepbystep solutions.

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

Control
The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable

Difference of two vectors
<u1, u2>  <v1, v2> = <u1  v1, u2  v2> or <u1, u2, u3>  <v1, v2, v3> = <u1  v1, u2  v2, u3  v3>

Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Inductive step
See Mathematical induction.

Interval
Connected subset of the real number line with at least two points, p. 4.

Inverse tangent function
The function y = tan1 x

kth term of a sequence
The kth expression in the sequence

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Quadratic equation in x
An equation that can be written in the form ax 2 + bx + c = 01a ? 02

Radius
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

Real number line
A horizontal line that represents the set of real numbers.

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

Terms of a sequence
The range elements of a sequence.

Vertical line
x = a.

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.