 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 7181 students have viewed full stepbystep solutions from this chapter.

Addition property of inequality
If u < v , then u + w < v + w

Directed angle
See Polar coordinates.

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Local extremum
A local maximum or a local minimum

Negative linear correlation
See Linear correlation.

Objective function
See Linear programming problem.

Order of magnitude (of n)
log n.

Parameter
See Parametric equations.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Reciprocal of a real number
See Multiplicative inverse of a real number.

Reflexive property of equality
a = a

Row operations
See Elementary row operations.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Slant line
A line that is neither horizontal nor vertical

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Variance
The square of the standard deviation.

Vertex of a cone
See Right circular cone.