: : . = : . . + : : ---- : Calculus and Analytic Geometry : : :
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. . .x f f+(x) . . . . . . . . . . . . . . . . x f f(x) . . . . . .
. . . . . . . . . . . . . . . L . . . . . . . . . . . . . x f f(x)
. . . . George Thomas and Ross Finney. Cal-culus and Analytic
Geometry. Addison-Wesley, Inc., USA, 9th ed., 1996. ISBN0201400154
. . x limxaf(x) . a x a a . a f(x) x< . f(x)=x limxx . f . y= x
. . . y= x (, )xy(, )y= xy= x . y= x y= x x x x . limx+x = ..
GeraldFolland. Real Analysis: Mod-ern Techniques and Their
Applications.Wiley, Inc., USA, 2nd ed., 1999. ISBN0201400000 f+(x)
x f x f f+(x) = limx+f(x + x) f(x)x( . ) . . . . L limxaf(x)
limxa+f(x), limxaf(x). L . f . . f(x) = x < x = x > f . .
y=(x)/(, )xy y=(x/)/ . [, ] f(x) x .limx f(x) = . limx+f(x) =
+.limxf(x) = limx+f(x). . . JonesPlotkin f f f x f(x) = limx f(x +
x) f(x)x( . ). . . . . f(x) = cos xf(x) = sin x y= sin x . y= cos x
. . . . . . . . . n . [a, b] y= f(x) b a xn . . . x x n a <
x< x< < xn< b.. . . xn b x a xybay= f(x)y= g(x) . y=
g(x) y= f(x) . . [a, b] c [a, b] f f(c) =b abaf(x)dx. . f(x) g(x)
[a, b] g f b a y= g(x) y= f(x) Charalambos Aliprantis and Kim
Bor-der. Infnite Dimensional Analysis.SpringerVerlag, Berlin,
Germany, 3rded., 2006. ISBN 3540295860A =ba[f(x) g(x)]dx. ( . ) . .
. . . f x ( )f(x) = limx f(x + x) f(x)x( . ). x f ( . ) . ( . ) . x
x x x + x=x ( . ) f(x) =limxxf(x) f(x)x x f I f . f(x) x f . . y= x
y= x . . . (, )xy(, )y= xy= x y= x . y= x ( .) .( . ) .g(x) = x
f(x) = x .xx = . x= x A =ba[f(x) g(x)]dx= ( +x x)dx . =[x +xx]=( +
)( + + ) . ( . ) . dcx = f(y) x = g(y)xyx =g(y) . [c, d] x = f(y) .
V=ba([R(x)][r(x)]) dx ( . ). r(x) R(x) . . r(x) ( . ) [a, b] . . ..
V=dc([R(y)][r(y)]) dy + ([ y]) dy + (y y) dy [y/y ] . . x=b x=a
y=f(x) George Thomas and Ross Finney.Calculus and Analytic
Geometry.Addison-Wesley, Inc., USA, 9th ed.,1996.ISBN 0201400154
[a, b] .( . ) . B A y= f(x) xyAaPxkBQ(xk) + (yk)xkykbxk b a y= f(x)
[a, b] f L =ba +(dydx)dx =ba + (f(x)) dx. ( . ) . . . dy/dx .( . )
y x dx/dy xyy= x . . . . . b a .( . ) . . dx(x )/. f . a + x = f b
x = g a + b x = h [, ) x= f(x)= /(x )/ [, ] . (, ] [, ] . dx(x
)/=limbbdx(x )/=limb[(b )/( )/]= . . . . . .x . . a x b y= R(x) x x
V=ba(R(x)) dx ( . ). George Thomas and Ross Finney.Calculus and
Analytic Geometry.Addison-Wesley, Inc., USA, 9th ed.,1996.ISBN
0201400154 . \def\@makechapterhead#1{% \vspace*{50\p@}% {\parindent
\z@ \raggedright \normalfont \ifnum \c@secnumdepth >\m@ne
\if@mainmatter \huge\bfseries \@chapapp\space \thechapter
\par\nobreak \vskip 20\p@ \fi \fi \interlinepenalty\@M \Huge
\bfseries #1\par\nobreak \vskip 40\p@ }}y . . c y d x = R(y) y y
V=dc(R(y))dy ( . ) . AB x y=x . . . y= x (, )xy(, )y= xy= x y= x .
y= x . . x=y+ f(y) = y + y= . y= y= y= . x . . b = A =dc[f(y)
g(y)]dy= [ +y y]dy=[y +yy]= . y . . f(x) x f x f f(x) = limxf(x +
x) f(x)x( . ) . . . f(x) = x + . . + cos xdx. x cos x ( x/) . cos
xdx . x= f(x)= x + . . f f(x) = x+ . x y=x . x . y x= y=(x + )(x
)(x + ) . . . f(x) =(x )(xx)x. . xyy= xf() = f() = f(x) . g(x)
=f(x)/x g . g() f . y= sin x cos x ( . )x yy . . y=x + . . limhof(
+h) f()h= x = y= f(x +x+) . . f(sin x cos x) =g(x ). f() g() = .
dy/dx . y= x + sin y. . x = t +t, y= tt. f() = g f . . g(x) = g() =
limx f(x)g(x)=f()g().. y= Arcsin x . . y= Arctan x . . y= Arcsin x
x + . y . f(x) = x + x ,. (f)() . y=cos x,. x y y y . y=x + x + ,.
x y y y a = b [a, b] f . baf(x)dx = ,. f(x) = [a, b] . . . . . . a
x b y= R(x) x x V=ba(R(x)) dx ( . ) x x y=x . . . . x c x=R(y) y y
y dV=dc(R(y)) dy ( . ) . . . f(x)g(x)dx ( . ) g f . xexdx, f(x) = x
. g(x) = ex exsin xdx . . . f x f(x) F(x) F(x) = f(x). x f f
f(x)dx. . . . f(x) = g(x) + g f . f F . C . F f . F f f F f(x)dx =
F(x) +C. . . . + cos xdx . . . . + cos xdx . . . + cos xdx . . . +
cos xdx . . f x . f(x) = x + f(x) = limx f(x + x) f(x)x= limx (x +
x) + (x + )x= limx x + xx + (x) + xx= limx xx + (x)x= limxx + (x)=
x f x . f f(x) = limx f(x + x) f(x)x( . ). x f () . ( . ) . x x x x
+ x = x ( . ) f(x) =limxxf(x) f(x)x x( . ). x = f(x) = x + I f .
f(x) x f . x = f f f(x) = x + . f f . f x f(x) = x f+(x) x f xf+(x)
= limx+f(x + x) f(x)x( . ) f+(x) = limxx+f(x) f(x)x x( . ) f(x) x f
x f . f(x) = limxf(x + x) f(x)x( . ) f(x) = limxxf(x) f(x)x x( . )
f . f(x) ={ x x < x x. . x = . () . f() .f() = ()limxf(x) =
limx(x ) = . limx+f(x) = limx+( x) = .f . f .limxf(x) = f() () .
limxf(x) = . f() = limxf( + x) f()x= limx(( + x) ) x= limx + x x= .
. I f . f(x) x f . f . f(x) = x + . . + cos xdx. x cos x ( x/) .
cos xdx . x= f(x)= x + . . f f(x) = x+ . f() = f() = f(x) . g(x)
=f(x)/x g . g(). y=x + . x y=x . x . y x= . y= Arcsin x . . y=
Arctan x . . y= Arcsin x x + . y . f(x) = x + x ,. (f)() . . . . .
. . . . I f . f(x) x f f(x) = . f f x . x + f(x) = limx f(x + x)
f(x)x= limx (x + x) + (x + )x= limx x + xx + (x) + xx= limx xx +
(x)x= limxx + (x)= x. f . x . x a x b y= R(x) V=ba(R(x)) dx ( . ) x
x y= x . . . . x n . [a, b] y=f(x) . b a xn . . . x x n y c y d x =
R(y) y V=dc(R(y)) dy ( . ) . . x x x x + x=x ( . ) ( . ) .f(x)
=limxxf(x) f(x)x x( . ) f . x= f(x)= x+ . x = . F . f(x) = g(x) +C
g f f F . F f f . F f f(x)dx = F(x) +C. . I f . f(x) x ff(x) = . f
x f(x) = x f x + . f f+(x) x f x f f+(x) = limx+f(x + x) f(x)x( . )
f+(x) = limxx+f(x) f(x)x x( . ) x f . f(x) x f f(x) = limxf(x + x)
f(x)x( . ) f(x) = limxxf(x) f(x)x x( . ). . . + cos xdx . . f x .
f(x)= x+ f(x) = limx f(x + x) f(x)x( . ) f ( . ) . . x f f(x) ={ x
x < x x . x = . .f()= (). () . f() limxf(x) = limx(x ) =
limx+f(x) = limx+( x) = ..limxf(x)=f() () . limxf(x)= . f . f f() =
limxf( + x) f()x= limx(( + x) ) x= limx + x x= limxxx . = limx= . .
I f . f(x) x f . f . \newcommand{\@tufte@lof@line}[2]{% \leftskip
0.0em \rightskip 0em \parfillskip 0em plus 1fil \parindent 0.0em
\@afterindenttrue \interlinepenalty\@M \leavevmode \@tempdima 2.0em
\advance\leftskip\@tempdima \null\nobreak\hskip -\leftskip
{#1}\nobreak\qquad\nobreak#2% \par% } x . . f() = () = . . f . . .
. : . y= (x )(x + ) = x.y= x / . .y= . f() = . dy/dx = xy y . .y(t)
= t x(t) = t + t . y= x . . (f)() = y= yy y . .y +yy y= . x . . f()
= () = . . f . . . . : . y= (x )(x + ) = x .y= x / . .y= . y= x . .
(f)() = y= yy y . .y +yy y= . . []. . [2]
CharalambosAliprantisandKimBorder. InfniteDimensional
Analysis.SpringerVerlag, Berlin, Germany, 3rd ed., 2006.ISBN
3540295860.[3] Gerald Folland.Real Analysis: Modern Techniques and
Their Applications.Wiley, Inc., USA, 2nd ed., 1999.ISBN
0201400000.[4] George Thomas and Ross Finney. Calculus and Analytic
Geometry. Addison-Wesley, Inc., USA, 9th ed., 1996.ISBN 0201400154.
Pendulum. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ideal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . Stability. . . . . . . . . . . . . . . . . . . . . . . . . .
. . Transform. . . . . . . . . . . . . . . . . . . . . . . . . . .
Global . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . Polynomial . . . . . . . . . . . . . . . . . . . .
Characteristic. . . . . . . . . . . . . . Imaginary. . . . . . . .
. . . . . . . . . . . . . . Angle. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . Acute. . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . Poem. . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . Romantic. . . . . . .
. . . . . . . . . . . . . . . . Persian. . . . . . . . . . . . . .
. Classic. . . . . . . . . . . . . . . . . . . . . . . . . .
Religious . . . . . . . . . . . . . . . . . . . . . . . . .
Ascension. . . . . . . . . . . . . . . . . . . . . . . . . . .
Operator. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arrow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . Bow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . Moment . . . . . . . . . . . . . . . . . . . . . . . . .
. . . Bevel . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . Spiral . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . Asymptotic. . . . . . . . . . . . . . . . . . . . .
. . . Cone. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . Equation. . . . . . . . . . . . . . . . . . . . . . . . . . .
. Linear . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . Curve. . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . Inequality. . . . . . . . . . . . . . . . . . . . . . . . .
Antiparallel . . . . . . . . . . . . . . . . . . . . . . . Map. . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Perfect. . . . . . . . . . . . . . . . . . . . . . . . . . .
Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. Additive. . . . . . . . . . . . . . . . . . . . . . . . . . .
Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Convergence. . . . . . . . . . . . . . . . . . . . . Calculus and
Analytic GeometryVahid DamanafshanInstructor Of The Kermanshah
University Of TechnologyKermanshah University Of Technology
Press2015
