- 12-8.Q1: The radius of convergence of a power series can be found using the ...
- 12-8.Q2: A geometric series converges if and only if ?
- 12-8.Q3: The Maclaurin series for cos x converges for what values of x?
- 12-8.Q4: The Taylor series for ln x expanded about x = 1 has what radius of ...
- 12-8.Q5: Write the first four nonzero terms of the Maclaurin series for tan1 x
- 12-8.Q6: Sketch a partial sum of the Maclaurin series for sine compared with...
- 12-8.Q7: Evaluate the integral: secx dx
- 12-8.Q8: Differentiate: y = tan x
- 12-8.Q9: Evaluate the integral: sec2x dx
- 12-8.Q10: Which two people are credited with having invented calculus?
- 12-8.1: For 14, a. Find the indicated partial sum. b. Use the Lagrange form...
- 12-8.2: For 14, a. Find the indicated partial sum. b. Use the Lagrange form...
- 12-8.3: For 14, a. Find the indicated partial sum. b. Use the Lagrange form...
- 12-8.4: For 14, a. Find the indicated partial sum. b. Use the Lagrange form...
- 12-8.5: For 58, use the Lagrange form of the remainder to find the number o...
- 12-8.6: For 58, use the Lagrange form of the remainder to find the number o...
- 12-8.7: For 58, use the Lagrange form of the remainder to find the number o...
- 12-8.8: For 58, use the Lagrange form of the remainder to find the number o...
- 12-8.9: For 910, calculate the value of c in the appropriate interval for w...
- 12-8.10: For 910, calculate the value of c in the appropriate interval for w...
- 12-8.11: For 1112, show that the hypotheses of the alternating series test a...
- 12-8.12: For 1112, show that the hypotheses of the alternating series test a...
- 12-8.13: p-Series 1: For the convergent p-series with p = 3, a. Find S10. Fi...
- 12-8.14: p-Series 2: For the convergent p-series with p = 1.05, a. Find S100...
- 12-8.15: Integral Bound Problem: Given the series a. Find the 11th partial s...
- 12-8.16: p-Series 3: The series is a p-series. Explain why the method of is ...
- 12-8.17: Geometric Series as an Upper Bound Problem: In Example 1 of this se...
- 12-8.18: Values of ex from Values of ex Problem: You can calculate the value...
- 12-8.19: Sin x for Any Argument Using a Value of x in [0, /4] Problem: The M...
- 12-8.20: The National Bureau of Standards Handbook of Mathematical Functions...
- 12-8.21: Derivation of the Lagrange Form of the Remainder: Earlier in this s...
- 12-8.22: A Pathological Function: Figure 12-8d shows the function Function f...
- 12-8.23: The Maclaurin Series for ex Converges to ex : shows that a Maclauri...
Solutions for Chapter 12-8: Error Analysis for SeriesThe Lagrange Error Bound
Full solutions for Calculus: Concepts and Applications | 2nd Edition
Chord of a conic
A line segment with endpoints on the conic
A fractional expression in which the numerator or denominator may contain fractions
See Cartesian coordinate system.
Direction angle of a vector
The angle that the vector makes with the positive x-axis
An identity involving a trigonometric function of 2u
The terms of the Fibonacci sequence.
Side opposite the right angle in a right triangle.
The complex number.
Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012 - ƒ1a - 0.00120.002
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.
An angle in standard position whose terminal side lies on an axis.
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.
Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.
Reflection across the y-axis
x, y and (-x,y) are reflections of each other across the y-axis.
Semiperimeter of a triangle
One-half of the sum of the lengths of the sides of a triangle.
symmetric about the x-axis
A graph in which (x, -y) is on the graph whenever (x, y) is; or a graph in which (r, -?) or (-r, ?, -?) is on the graph whenever (r, ?) is
A set of equations or inequalities.
A visualization of the relationships among events within a sample space.
See n factorial.