 8.3.1: Show that if x > 0 and ifn > 2x, thenI ( X xn )I2xn+1eX_ 1++...+ ...
 8.3.2: Calculate e correct to 5 decimal places.
 8.3.3: Show that if 0 ::: x ::: a and n EN, thenx xn X xnl eaxn1++...+ ...
 8.3.4: Showthatif n ~ 2, then( 1 1 ) e o < en!  1+ 1+  + .. . +  n! < ...
 8.3.5: Ifx ~ 0 andn E N, showthat1= 1 x+x 2 x 3 +...+(x) nl +(._x)n ...
 8.3.6: Usetheformula in theprecedingexerciseto calculateIn 1.1andIn 1.4acc...
 8.3.7: Showthat In(e/2) = 1 In 2. Use this result to calculate In 2 accur...
 8.3.8: Let I : JR+ JR be such that I' (x) = I (x) for all x e JR. Show th...
 8.3.9: Let ak > 0 for k = 1, "', n and let A := (a1+... + an)/n be the ari...
 8.3.10: Evaluate L'(I) by using the sequence (1 + l/n) and the fact that e ...
 8.3.11: Estaglish the assertions in Theorem 8.3.11.
 8.3.12: Establish the assertions in Theorem 8.3.12.
 8.3.13: (a)Establish the assertions in Theorem 8.3.12.Show that if ex> 0, t...
 8.3.14: Prove that if a > 0, a =F 1, then alogax= x for all x e (0,00) and ...
 8.3.15: If a > 0, a =F 1, show that the function x 1+logox is differentiab...
 8.3.16: If a > 0, a =F1, and x and y belong to (0,00), prove that logo(xy) ...
 8.3.17: If a > 0, a =F 1, and b > 0, b =F 1, show that(In b logox = In a)10...
Solutions for Chapter 8.3: The Exponential and Logarithmic Functions
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 8.3: The Exponential and Logarithmic Functions
Get Full SolutionsIntroduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Chapter 8.3: The Exponential and Logarithmic Functions includes 17 full stepbystep solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Since 17 problems in chapter 8.3: The Exponential and Logarithmic Functions have been answered, more than 3115 students have viewed full stepbystep solutions from this chapter.

Associative properties
a + (b + c) = (a + b) + c, a(bc) = (ab)c.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Complex number
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)

Demand curve
p = g(x), where x represents demand and p represents price

Halfangle identity
Identity involving a trigonometric function of u/2.

Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2  x 1, y2  y19>

Horizontal translation
A shift of a graph to the left or right.

Integers
The numbers . . ., 3, 2, 1, 0,1,2,...2

Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.

Measure of center
A measure of the typical, middle, or average value for a data set

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Objective function
See Linear programming problem.

Period
See Periodic function.

Real zeros
Zeros of a function that are real numbers.

Replication
The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.

Slant asymptote
An end behavior asymptote that is a slant line

Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n  12d4,

Variation
See Power function.
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