- 9.1: Cantor Set The Cantor set (Georg Cantor, 18451918) is a subset of t...
- 9.2: Using Sequences (a) Given that and show that is convergent and (b) ...
- 9.3: Using a Series It can be shown that n11n2 262 [see Section 9.3, pag...
- 9.4: Finding a Limit Let be an equilateral triangle with sides of length...
- 9.5: Using Center of Gravity Identical blocks of unit length are stacked...
- 9.6: Using Power Series (a) Consider the power series in which the coeff...
- 9.7: Finding Sums of Series (a) Find a power series for the function cen...
- 9.8: Using the Alternating Series Test The graph of the function is show...
- 9.9: Conditional and Absolute Convergence For what values of the positiv...
- 9.10: Proof (a) Consider the following sequence of numbers defined recurs...
- 9.11: Proof Let be a sequence of positive numbers satisfying Prove that t...
- 9.12: . Using a Series Consider the infinite series (a) Find the first fi...
- 9.13: Deriving Identities Derive each identity using the appropriate geom...
- 9.14: Population Consider an idealized population with the characteristic...
- 9.15: Spheres Imagine you are stacking an infinite number of spheres of d...
- 9.16: Determining Convergence or Divergence (a) Determine the convergence...
Solutions for Chapter 9: Calculus 10th Edition
Full solutions for Calculus | 10th Edition
An angle whose measure is between 0° and 90°
The measure of an angle in degrees, minutes, and seconds
The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant
Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0
Linear regression equation
Equation of a linear regression line
Magnitude of a vector
The magnitude of <a, b> is 2a2 + b2. The magnitude of <a, b, c> is 2a2 + b2 + c2
See Absolute value of a complex number.
A triangle in which one angle is greater than 90°.
Power rule of logarithms
logb Rc = c logb R, R 7 0.
Product of complex numbers
(a + bi)(c + di) = (ac - bd) + (ad + bc)i
Computer-generated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.
Real part of a complex number
See Complex number.
A set of ordered pairs of real numbers.
Solve by substitution
Method for solving systems of linear equations.
A set of equations or inequalities.
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.
See Conversion factor.