 8.1: Find the length of the curve. y 16 x 2 432 0 x 3y
 8.2: Find the length of the curve. y 2 ln(sin 12 x) 3 x y
 8.3: (a) Find the length of the curve (b) Find the area of the surface o...
 8.4: (a) The curve , , is rotated about the axis. Find the area of the ...
 8.5: Use Simpsons Rule with to estimate the length of the sine curve , .
 8.6: Use Simpsons Rule with to estimate the area of the surface obtained...
 8.7: Find the length of the curve
 8.8: Find the area of the surface obtained by rotating the curve in Exer...
 8.9: A gate in an irrigation canal is constructed in the form of a trape...
 8.10: A trough is filled with water and its vertical ends have the shape ...
 8.11: Find the centroid of the region bounded by the given curves.
 8.12: Find the centroid of the region bounded by the given curves.
 8.13: Find the centroid of the region shown
 8.14: Find the centroid of the region shown
 8.15: Find the volume obtained when the circle of radius 1 with center is...
 8.16: Use the Theorem of Pappus and the fact that the volume of a sphere ...
 8.17: The demand function for a commodity is given by Find the consumer s...
 8.18: After a 6mg injection of dye into a heart, the readings of dye con...
 8.19: (a) Explain why the function is a probability density function. (b)...
 8.20: Lengths of human pregnancies are normally distributed with mean 268...
 8.21: The length of time spent waiting in line at a certain bank is model...
Solutions for Chapter 8: Calculus, 7th Edition
Full solutions for Calculus,  7th Edition
ISBN: 9780538497817
Solutions for Chapter 8
Get Full SolutionsChapter 8 includes 21 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus,, edition: 7. Calculus, was written by and is associated to the ISBN: 9780538497817. Since 21 problems in chapter 8 have been answered, more than 7141 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Associative properties
a + (b + c) = (a + b) + c, a(bc) = (ab)c.

Circular functions
Trigonometric functions when applied to real numbers are circular functions

Conversion factor
A ratio equal to 1, used for unit conversion

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Even function
A function whose graph is symmetric about the yaxis for all x in the domain of ƒ.

Irrational numbers
Real numbers that are not rational, p. 2.

Jump discontinuity at x a
limx:a  ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

Leastsquares line
See Linear regression line.

Multiplication principle of counting
A principle used to find the number of ways an event can occur.

Natural logarithm
A logarithm with base e.

Onetoone rule of exponents
x = y if and only if bx = by.

Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc  ad c2 + d2 i

Quotient rule of logarithms
logb a R S b = logb R  logb S, R > 0, S > 0

Right triangle
A triangle with a 90° angle.

Subtraction
a  b = a + (b)

Transformation
A function that maps real numbers to real numbers.

Vector
An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

Whole numbers
The numbers 0, 1, 2, 3, ... .

Wrapping function
The function that associates points on the unit circle with points on the real number line

yintercept
A point that lies on both the graph and the yaxis.