 11.1.1.1: Show that the following equations have at least one solution in the...
 11.1.1.2: Find intervals containing solutions to the following equations. a. ...
 11.1.1.3: Show that f (x) is 0 at least once in the given intervals. a. f (x)...
 11.1.1.4: Find maxaxb  f (x) for the following functions and intervals. a. ...
 11.1.1.5: Use the Intermediate Value Theorem and Rolles Theorem to show that ...
 11.1.1.6: Suppose f C[a, b] and f (x) exists on (a, b). Show that if f (x) = ...
 11.1.1.7: Let f (x) = x 3. a. Find the second Taylor polynomial P2(x) about x...
 11.1.1.8: Find the third Taylor polynomial P3(x) for the function f (x) = x +...
 11.1.1.9: Find the third Taylor polynomial P3(x) for the function f (x) = x +...
 11.1.1.10: Repeat Exercise 9 using x0 = /6.
 11.1.1.11: Find the third Taylor polynomial P3(x) for the function f (x) = (x ...
 11.1.1.12: Let f (x) = 2x cos(2x) (x 2)2 and x0 = 0. a. Find the third Taylor ...
 11.1.1.13: Find the fourth Taylor polynomial P4(x) for the function f (x) = xe...
 11.1.1.14: Use the error term of a Taylor polynomial to estimate the error inv...
 11.1.1.15: Use a Taylor polynomial about /4 to approximate cos 42 to an accura...
 11.1.1.16: Let f (x) = ex/2 sin(x/3). Use Maple to determine the following. a....
 11.1.1.17: Let f (x) = ln(x 2 + 2). Use Maple to determine the following. a. T...
 11.1.1.18: Let f (x) = (1 x)1 and x0 = 0. Find the nth Taylor polynomial Pn (x...
 11.1.1.19: Let f (x) = ex and x0 = 0. Find the nth Taylor polynomial Pn (x) fo...
 11.1.1.20: Find the nth Maclaurin polynomial Pn (x) for f (x) = arctan x.
 11.1.1.21: The polynomial P2(x) = 1 1 2 x 2 is to be used to approximate f (x)...
 11.1.1.22: The nth Taylor polynomial for a function f at x0 is sometimes refer...
 11.1.1.23: A Maclaurin polynomial for ex is used to give the approximation 2.5...
 11.1.1.24: The error function defined by erf(x) = 2 x 0 et 2 dt gives the prob...
 11.1.1.25: A function f : [a, b] R is said to satisfy a Lipschitz condition wi...
 11.1.1.26: Suppose f C[a, b], that x1 and x2 are in [a, b], and that c1 and c2...
 11.1.1.27: Suppose f C[a, b], that x1 and x2 are in [a, b], and that c1 and c2...
Solutions for Chapter 11: Review of Calculus
Full solutions for Numerical Analysis (Available Titles CengageNOW)  8th Edition
ISBN: 9780534392000
Solutions for Chapter 11: Review of Calculus
Get Full SolutionsThis textbook survival guide was created for the textbook: Numerical Analysis (Available Titles CengageNOW) , edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Numerical Analysis (Available Titles CengageNOW) was written by and is associated to the ISBN: 9780534392000. Chapter 11: Review of Calculus includes 27 full stepbystep solutions. Since 27 problems in chapter 11: Review of Calculus have been answered, more than 11903 students have viewed full stepbystep solutions from this chapter.

Argument of a complex number
The argument of a + bi is the direction angle of the vector {a,b}.

Bounded below
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.

Commutative properties
a + b = b + a ab = ba

Cosecant
The function y = csc x

Cubic
A degree 3 polynomial function

Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic

Ellipsoid of revolution
A surface generated by rotating an ellipse about its major axis

Endpoint of an interval
A real number that represents one “end” of an interval.

Finite series
Sum of a finite number of terms.

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Index of summation
See Summation notation.

Negative numbers
Real numbers shown to the left of the origin on a number line.

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

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

Radian measure
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.

Real zeros
Zeros of a function that are real numbers.

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Regression model
An equation found by regression and which can be used to predict unknown values.

Vertical stretch or shrink
See Stretch, Shrink.

ycoordinate
The directed distance from the xaxis xzplane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.