(a) Prove that g x 5 decreasing in this interval in .NET

Printing QR Code JIS X 0510 in .NET (a) Prove that g x 5 decreasing in this interval

3.5. (a) Prove that g x 5 decreasing in this interval
Decoding QR-Code In .NET Framework
Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in VS .NET applications.
QR Code JIS X 0510 Creator In Visual Studio .NET
Using Barcode printer for VS .NET Control to generate, create QR image in Visual Studio .NET applications.
p 9 x is strictly decreasing in 0 @ x @ 9. (c) Does g x have a single-valued inverse
Reading QR Code JIS X 0510 In .NET
Using Barcode recognizer for .NET framework Control to read, scan read, scan image in .NET framework applications.
Encoding Bar Code In .NET Framework
Using Barcode creation for .NET framework Control to generate, create barcode image in .NET framework applications.
(b) Is it monotonic
Barcode Decoder In .NET
Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in VS .NET applications.
Printing QR-Code In Visual C#
Using Barcode encoder for Visual Studio .NET Control to generate, create QR-Code image in Visual Studio .NET applications.
(a) p strictly decreasing 1 > g x g x is If x1 < x2 then 9 x1 > 9 x2 , p p if g x p 2 whenever x1 < x2 . 9 x1 > 9 x2 , 5 9 x1 > 5 9 x2 showing that g x is strictly decreasing. (b) Yes, any strictly decreasing function is also monotonic decreasing, since if g x1 > g x2 it is also true that g x1 A g x2 . However, if g x is monotonic decreasing, it is not necessarily strictly decreasing. p p (c) If y 5 9 x, then y 5 9 x or squaring, x 16 10y y2 y 2 8 y and x is a single-valued function of y, i.e., the inverse function is single-valued. In general, any strictly decreasing (or increasing) function has a single-valued inverse (see Theorem 6, Page 47). The results of this problem can be interpreted graphically using the gure of Problem 3.4.
Creating Quick Response Code In Visual Studio .NET
Using Barcode encoder for ASP.NET Control to generate, create QR Code image in ASP.NET applications.
Generate QR Code 2d Barcode In VB.NET
Using Barcode drawer for .NET framework Control to generate, create QR Code image in .NET applications.
& 3.6. Construct graphs for the functions integer @ x. (a) f x
1D Creator In Visual Studio .NET
Using Barcode creator for .NET Control to generate, create Linear image in .NET framework applications.
Barcode Generation In Visual Studio .NET
Using Barcode generator for .NET Control to generate, create bar code image in .NET framework applications.
x sin 1=x; 0;
Encode Barcode In Visual Studio .NET
Using Barcode creation for .NET Control to generate, create bar code image in VS .NET applications.
Making ANSI/AIM ITF 25 In .NET
Using Barcode generator for .NET Control to generate, create ITF image in .NET applications.
x>0 , x 0
EAN 13 Creation In Java
Using Barcode creator for BIRT Control to generate, create EAN13 image in Eclipse BIRT applications.
Creating Bar Code In VS .NET
Using Barcode maker for Reporting Service Control to generate, create barcode image in Reporting Service applications.
(b) f x x greatest
Code 128A Drawer In Objective-C
Using Barcode generation for iPad Control to generate, create Code 128B image in iPad applications.
UPC A Drawer In .NET
Using Barcode creator for ASP.NET Control to generate, create GS1 - 12 image in ASP.NET applications.
(a) The required graph is shown in Fig. 3-8. Since jx sin 1=xj @ jxj, the graph is included between y x and y x. Note that f x 0 when sin 1=x 0 or 1=x ; m, m 1; 2; 3; 4; . . . ; i.e., where x 1=; 1=2; 1=3; . . . . The curve oscillates in nitely often between x 1= and x 0. p (b) The required graph is shown in Fig. 3-9. If 1 @ x < 2, then x 1. Thus 1:8 1, 2 1, 1:99999 1. However, 2 2. Similarly for 2 @ x < 3, x 2, etc. Thus there are jumps at the integers. The function is sometimes called the staircase function or step function.
UPC - 13 Maker In None
Using Barcode creation for Online Control to generate, create EAN 13 image in Online applications.
Barcode Decoder In Java
Using Barcode Control SDK for BIRT reports Control to generate, create, read, scan barcode image in BIRT applications.
3.7. (a) Construct the graph of f x tan x. (b) Construct the graph of some of the in nite number of branches available for a de nition of tan 1 x. (c) Show graphically why the relationship of x
UPC Code Reader In VS .NET
Using Barcode reader for .NET framework Control to read, scan read, scan image in VS .NET applications.
Encode Code 128 Code Set A In None
Using Barcode maker for Software Control to generate, create Code 128 Code Set A image in Software applications.
CHAP. 3]
FUNCTIONS, LIMITS, AND CONTINUITY
f (x)
f (x)
1/2p
_3 _2 _1
1 2 3 4 5
Fig. 3-8
Fig. 3-9
to y is multivalued. (d) Indicate possible principal values for tan 1 x. (e) Using your choice, evaluate tan 1 1 .
(a) The graph of f x tan x appears in Fig. 3-10 below.
y = f (x) = tan x
(x) = tan 1x
3p/2 p
p/2 _ p _ p/2 p/2 p 3p/2 2p
_ p/2 _p
Fig. 3-10
Fig. 3-11
(b) The required graph is obtained by interchanging the x and y axes in the graph of (a). The result, with axes oriented as usual, appears in Fig. 3-11 above. (c) In Fig. 3-11 of (b), any vertical line meets the graph in in nitely many points. Thus, the relation of y to x is multivalued and in nitely many branches are available for the purpose of de ning tan 1 x.
(d) To de ne tan 1 x as a single-valued function, it is clear from the graph that we can only do so by restricting its value to any of the following: =2 < tan 1 x < =2; =2 < tan 1 x < 3=2, etc. We shall agree to take the rst as de ning the principal value. Note that no matter which branch is used to de ne tan 1 x, the resulting function is strictly increasing. (e) tan 1 1 =4 is the only value lying between =2 and =2, i.e., it is the principal value according to our choice in d .
3.8. Show that f x
If y
p p x 1 then x 1 y 1 x or squaring, x 1 2 y2 2 x 1 y 1 x 0, a polynomial x 1 equation in y whose coe cients are polynomials in x. Thus f x is an algebraic function. However, it is not the quotient of two polynomials, so that it is an irrational algebraic function.
Copyright © OnBarcode.com . All rights reserved.