- 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
A flaw in the design of a sampling process that systematically causes the sample to differ from the population with respect to the statistic being measured. Undercoverage bias results when the sample systematically excludes one or more segments of the population. Voluntary response bias results when a sample consists only of those who volunteer their responses. Response bias results when the sampling design intentionally or unintentionally influences the responses
Conic section (or conic)
A curve obtained by intersecting a double-napped right circular cone with a plane
Direction vector for a line
A vector in the direction of a line in three-dimensional space
Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic
Graph of a function ƒ
The set of all points in the coordinate plane corresponding to the pairs (x, ƒ(x)) for x in the domain of ƒ.
Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.
Index of summation
See Summation notation.
A special case of a limit that does not exist.
Integrable over [a, b] Lba
ƒ1x2 dx exists.
A distribution of data shaped like the normal curve.
See Additive inverse of a real number and Additive inverse of a complex number.
Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.
A transformation that leaves the basic shape of a graph unchanged.
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the right-hand end point of each subinterval.
Solve an equation or inequality
To find all solutions of the equation or inequality
Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.
A circle with radius 1 centered at the origin.
Vertical stretch or shrink
See Stretch, Shrink.
A point that lies on both the graph and the y-axis.
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