 6.1.1: Use the definition to find the derivative of each of the following ...
 6.1.2: Showthat I (x) := x 1/3,x E JR,is not differentiable at x =O.
 6.1.3: Prove Theorem 6.1.3(a), (b).
 6.1.4: Let I :JR~' JRbe defined by I(x) := x2 for x rational, I(x) := 0 fo...
 6.1.5: Differentiate and simplify:x(a) l(x):="2'l+x(c) h(x):= (sinxk)m f...
 6.1.6: Letn E Nandlet I : JR+JRbe definedby I(x) := xn forx ~ 0 andI(x) ...
 6.1.7: Suppose that I : JR+JRis differentiable at c and that I(c) = O.Sh...
 6.1.8: Determine where each of the following functionsfrom JRto JRis diffe...
 6.1.9: Prove that if I : JR+JRis an even function [that is, I( x) =I(x)...
 6.1.10: Let g : JR+ JRbe defined by g(x) := x2 sinO/x2) for x 1=0, and g(...
 6.1.11: Assume that there exists a function L : (0,00) + JRsuch that L'(x...
 6.1.12: If r > 0 is a rational number, let I : JR+ JRbe defined by I(x) :...
 6.1.13: If I : JR+ JRis differentiable at c E JR,show thatI'(c) = lim(n{f...
 6.1.14: Giventhat the functionh(x) := x3 + 2x + 1for x E JRhas an inverse h...
 6.1.15: Given that the restriction of the cosine function cos to I := [0, 1...
 6.1.16: Given that the restriction of the tangent function tan to I := (1l...
 6.1.17: Let I : I + JRbe differentiable at eEl. Establish the Straddle Le...
Solutions for Chapter 6.1: The Derivative
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 6.1: The Derivative
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Since 17 problems in chapter 6.1: The Derivative have been answered, more than 8784 students have viewed full stepbystep solutions from this chapter. Chapter 6.1: The Derivative includes 17 full stepbystep solutions.

Binomial coefficients
The numbers in Pascalâ€™s triangle: nCr = anrb = n!r!1n  r2!

Branches
The two separate curves that make up a hyperbola

Constant term
See Polynomial function

Degree
Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution

Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

Inverse tangent function
The function y = tan1 x

Leading coefficient
See Polynomial function in x

Multiplication property of equality
If u = v and w = z, then uw = vz

nth root
See Principal nth root

Ordered pair
A pair of real numbers (x, y), p. 12.

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Radicand
See Radical.

Shrink of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal shrink) by the constant 1/c or all of the ycoordinates (vertical shrink) by the constant c, 0 < c < 1.

Solve graphically
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

Speed
The magnitude of the velocity vector, given by distance/time.

Symmetric about the yaxis
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

Synthetic division
A procedure used to divide a polynomial by a linear factor, x  a

Transitive property
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.

Trigonometric form of a complex number
r(cos ? + i sin ?)

Unit ratio
See Conversion factor.