sql server reporting services barcode font Approximate in Software

Painting Denso QR Bar Code in Software Approximate

EXAMPLE 18 Approximate
Read QR Code JIS X 0510 In None
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
Generating Denso QR Bar Code In None
Using Barcode maker for Software Control to generate, create Denso QR Bar Code image in Software applications.
/2
Scanning QR In None
Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications.
Print QR Code JIS X 0510 In C#
Using Barcode printer for VS .NET Control to generate, create Denso QR Bar Code image in .NET applications.
sin x dx using the trapezoidal rule.
Make Denso QR Bar Code In .NET Framework
Using Barcode generation for ASP.NET Control to generate, create Denso QR Bar Code image in ASP.NET applications.
Draw Quick Response Code In VS .NET
Using Barcode encoder for VS .NET Control to generate, create QR Code ISO/IEC18004 image in VS .NET applications.
f[x_] = Sin[x]; a = 0; b = o/2; n = 100; x = (b a)/n; x[i_] = a + i * x;
Draw QR In Visual Basic .NET
Using Barcode drawer for Visual Studio .NET Control to generate, create QR Code image in Visual Studio .NET applications.
Bar Code Creation In None
Using Barcode generation for Software Control to generate, create bar code image in Software applications.
n-1 approximation = x f[a]+ 2 f[x[i]]+ f[b] //N 2 i=1 0.999979
Generating Code-128 In None
Using Barcode printer for Software Control to generate, create ANSI/AIM Code 128 image in Software applications.
Generate GTIN - 13 In None
Using Barcode printer for Software Control to generate, create EAN / UCC - 13 image in Software applications.
SOLVED PROBLEMS
Paint Bar Code In None
Using Barcode creation for Software Control to generate, create bar code image in Software applications.
UCC - 12 Maker In None
Using Barcode generation for Software Control to generate, create UPCA image in Software applications.
9.22 Compute the Riemann sums of f ( x ) = x e x x over the interval [0, 2] using (a) the left endpoint of each subinterval. (b) the right endpoint of each subinterval. (c) the midpoint of each subinterval. 2 Compare with Mathematica s approximation to the integral f ( x )dx.
Create Leitcode In None
Using Barcode generation for Software Control to generate, create Leitcode image in Software applications.
Print Code 3/9 In Java
Using Barcode generator for Java Control to generate, create Code 39 image in Java applications.
SOLUTION
UPC A Generator In .NET Framework
Using Barcode creator for ASP.NET Control to generate, create UPC Code image in ASP.NET applications.
ECC200 Creator In None
Using Barcode generator for Office Word Control to generate, create ECC200 image in Office Word applications.
f[x_] = x x a = 0; b = 2;
Code 128C Creator In Objective-C
Using Barcode encoder for iPhone Control to generate, create Code 128C image in iPhone applications.
Print Bar Code In Java
Using Barcode printer for Java Control to generate, create barcode image in Java applications.
f[x] x //N
2D Barcode Printer In Visual Basic .NET
Using Barcode encoder for .NET Control to generate, create Matrix Barcode image in Visual Studio .NET applications.
Bar Code Printer In C#
Using Barcode printer for Visual Studio .NET Control to generate, create bar code image in .NET applications.
Mathematica s approximation.
Integral Calculus
n = 100; x =(b a) / n; xstar[i_] = a + (i 1) x;
f[xstar[i]] x
Left endpoint approximation.
10.0328 xstar[i_] = a + i x;
f[xstar[i]] x
Right endpoint approximation.
10.4508 xstar[i_] = a + (i .5) x;
f[xstar[i]] x
Midpoint approximation.
9.23 Approximate 1 x ln x dx using the trapezoidal rule with n = 100 and compare the result with Mathematica s approximation.
SOLUTION
f[x_]= x Log[x]; a = 1; b = 2; n = 100; x = (b a) / n; x[i_] = a + i x;
n-1 approximation = x f[a]+ 2 f[x[i]]+ f[b] //N 2 i=1 0.6363
f[x] x //N
The error of 0.000006 is less than 0.001%.
9.24 Compute the lower and upper Riemann sums for the function f(x) = x2 on the interval [0, 1] for n = 2, 4, 8, 16, . . . , 220 subintervals. Explain the behavior of the approximations in terms of the 1 integral x 2 dx .
SOLUTION
f[x_]= x2; a = 0; b = 1; n = 2m; x =(b a) / n; nn = PaddedForm[n, 10]; n temp1 = PaddedForm N f[a +(i 1) x] x ,{8,6} ; i=1 n temp2 = PaddedForm N f[a + i x] x ,{8,6} ; i=1 list = Table[{nn, temp1, temp2}, {m, 1, 20}]; TableForm[list, TableSpacing {1, 5}, TableHeadings {None, {" n", " Lower", " Upper"}}]
Integral Calculus
n 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
Lower 0.125000 0.218750 0.273438 0.302734 0.317871 0.325562 0.329437 0.331383 0.332357 0.332845 0.333089 0.333211 0.333272 0.333303 0.333318 0.333326 0.333330 0.333331 0.333332 0.333333
Upper 0.625000 0.468750 0.398438 0.365234 0.349121 0.341187 0.337250 0.335289 0.334311 0.333822 0.333578 0.333455 0.333394 0.333364 0.333349 0.333341 0.333337 0.333335 0.333334 0.333334
As n gets larger, the lower sums increase, approaching a limit of 1 , and the upper sums decrease, also 3 approaching 1 . 3 1 x2 x
9.25 Compute an approximation of e x dx using the trapezoidal rule with 10, 50, and 100 subintervals. 0 Compare with Mathematica s approximation.
SOLUTION
f[x_] = Exp[x2]; a = 0; b = 1;
f[x] x //N
This is Mathematica s approximation.
1.46265 x = (b a)/n; x[i_] = a + i * x; n = 10
n 1 approximation = x f[a]+ 2 f[x[i]]+ f[b] //N 2 i=1
1.46717 n = 50
n 1 approximation = x f[a]+ 2 f[x[i]]+ f[b] //N 2 i=1
Error = 0.00452.
1.46283 n = 100
n 1 approximation = x f[a]+ 2 f[x[i]]+ f[b] //N 2 i=1
Error = 0.00018.
Error = 0.00005.
CH AP TE R 10
Multivariate Calculus
10.1 Partial Derivatives
The commands D, , and Derivative discussed in 8 are actually commands for computing partial derivatives. Of course, if there is only one variable present in a function, the partial derivative becomes an ordinary derivative. If two or more variables are present, however, all variables other than the one specified are treated as constants. In the following descriptions, f stands for a function of several variables.
D[f, x] or x f (on the Basic Math Input palette) returns f/ x, the partial derivative of f with respect to x. D[f,(x, n}] or {x, n}f returns nf/ xn, the nth order partial derivative of f with respect to x. kf D[f, x1, x2,..., xk] or x1, x2, ..., xkf returns the mixed partial derivative x1 x2 ... x k {x1, n1}, {x2, n2},..., {xk, nk}] or {x , n }, {x , n }, ..., {x , n }f returns the partial D[f, 1 1 2 2 k k nf[x1, x2, ..., x k ] where n 1 + n 2 + ... + n k = n. derivative n n1 n2 ... xk x1 x2 k
For convenience, an invisible comma may be used to separate variables in the partial derivative symbol. An invisible comma is entered by the three-key sequence [ESC] [.] [ESC]. An invisible comma works like an ordinary comma, but is hidden from the display.
Copyright © OnBarcode.com . All rights reserved.