«MACLAURIN'S SERIES» 관련 영어 책
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1
Higher Engineering Mathematics
Develop a series for sinhx using Maclaurin's series. f(x)=sinhx f(0)=sinh0= e0−e−
02=0 f(x)= coshx f(0)= cosh0 = e0+e−02 = 1 f(x)=sinhx f(0)=sinh0=0 f(x)=coshx f(0
)=cosh0= 1 fiv(x)= sinhx fiv(0)= sinh0 = 0 fv(x)=coshx fv(0)=cosh0=1 ...
2
Understanding Engineering Mathematics
Now try the following Practice Exercise Practice Exercise 97 Further problems on
Maclaurin's series (answers on page 1118) 1. Determine the first four terms of the
power series for sin 2x using Maclaurin's series. 2. Use Maclaurin's series to ...
3
Newnes Engineering Mathematics Pocket Book
x2 X4 and coshx:1+E+E+--. Using a series, called Maclaurin's series, mixed
functions containing, say, algebraic, trigonometric and exponential functions, may
be expressed solely as algebraic functions, and differentiation and integration
can ...
4
GCE A-level Mathematics Challenging Drill Questions ...
Given that y I (sin'1 x)2, show that 121 (1 Xlidxi —4y 2 and (1—X2)d—l2/—Xfl:2
dx dx By further differentiation, find the Maclaurin's series of y up to and including
the term in x4. 3 x Show how the expansion sin'1 x z x +? may be used to verify ...
Thomas Bond, Chris Hughes,
2013
5
Mathematics for Electrical Technicians 4/5: Level 4-5
The uses of Maclaurin's series include expressing mixed functions, containing
some or all of trigonometric, exponential, algebraic and logarithmic terms, in a
form where such techniques as Newton's method (see Chapter 2), or
approximate ...
J. O. Bird, A. J. C. May,
2014
6
Textbook of Differential Calculus
This is called Maclaurin's series. Corollary 1 Let y = f(x), y, = f(x), y2 = f'(x), ...
Putting x = 0, we write /(0) = (j)o, /'(0) = CvOo, f'(0) = (y2)0, ... Therefore, x2, . x> y
= f(x) = (y)o+x(y1)0 +—(y2)0+—(yi)0+--- This is the another form of Maclaurin's
series ...
Ahsan Akhtar, Sabiha Ahsan,
2004
Maclaurin's series is a special case of Taylor's series and Taylor's theorem with
the Lagranges form of remainder is a simple variation law of the mean. Both the
series expansions of a function represent that function for those values and only ...
8
Engineering Mathematics - I
Thus putting a = 0 and h = x in Taylor's theorem, we get f(x) = f(0)+xf'(0)+^ '"(0) + ^
- HO) + ... + .n-1 (n-1) f(n)(0) + Rn D) Maclaurin's Series If Rn — » 0 as n — > °°
then Maclaurin's theorem assumes the form of Maclaurin's series and it is given ...
9
Engineering Mathematics Pocket Book
Substituting these values into the Maclaurin's series gives: f(x) ln( x) x() x!() x ! ) x!
() x ! () 1 0 1 21 3 2 4 6 5 24 2 3 4 5 ( i.e. ln(1x)xx2x3x4x5 ... 2 3 4 5 Application:
Find the expansion of (2 x)4 using Maclaurin's series f(x) ( x) f() f(x) ( x) f() () 32 f(x
) ...
10
GCE A-level Mathematics Challenging Drill Questions ...
2 (1—X2)(%j :4y d_2Y_ Q_ and 1—xZ X ( )dxz dX 2 By further differentiation, find
the Maclaurin's series of y up to and including the term in x4. x3 Show how the
expansion sin'1 Xz X+€ may be used to verify the answer obtained above. d .
Thomas Bond, Chris Hughes,
2013