Page 12 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

noEPk;soh dk rfDs

B'N 2H pj[uoh cbB (Functions of Many Variable)^i/eo uo okPh u, d' uo okPhnK x ns/
y T[Zs/ nkfPqs j?, T[d'A u = f (x, y) pj[uoh cbB ejkT[Adk j?.
3H ;gPN cbB (Explicit Function)^cbB y = f (x) fJZe ;gPN cbB ejkT[Adk j? i/eo y
B{z x d/ ;[szso gdK d/ o{g ftZu fbyDk ;zGt j't/.
x
2
fit/AL y = x + 2x – 5, y = cos x, y = nkfd.
+
1 x 2
4H n;gPN cbB (Implicit Function)^cbB y = f (x) fJZe n;gPN cbB ejkT[Adk j?
i/eo y B{z x d/ ;[szso gdK d/ o{g ftZu fbyDk ;zGt Bk j't/.
T[dkjoD ti'A^
2
2
Y = x sin ( x + y), Gkt f (x, y) = 0, x + y – xy = 0 nkfd.
5H ;w cbB (Even Function)^wzB fbU y = f (x) uo x dk e'Jh cbB j?.
i/eo f (^x) = f (x)

Gkt i/eo f (x) ftZu x d/ ;EkB s/ -x oZyD s/ cbB dk fuzBQ Bk pdb/ sK T[j ;w cbB
ejkT[Adk j?.

T[dkjoD ti'A^
f (x) = cos x = cos (-x) = f (^x)
6H fpyw cbB (Odd Function)^wzB fbU y = f (x) uo x dk e'Jh cbB j?.
3
3
T[dkjoD ti'A^ f (x) = x = ^ (^x ) = ^f (^x).
i/eo f (^x) = ^f (x) Gkt i/eo f (x) ftZu x d/ ;EkB s/ ^x oZyD s/ cbB dk fuzBQ pdb
ikt/ sK T[j fpyw cbB ejkT[Adk j?.
7H phie cbB (Algebraic Function)^uo okPh x dh ftfGzB ;zfynkswe xksK tkbk
nfijk cbB fi; ftZu gdK dh ;zfynk fBPfus j't/, phie cbB ejkT[Adk j?.
T[dkjoD ti'A^

phie cbB jB.
8H gfow/: cbB (Rational Function)^fJZe fGzB d/ o{g ftZu ftnes ehsk frnk nfijk
cbB fi;d/ nzP ns/ jo d'B'A jh g{oD nze xksK tkb/ phie ftnzie j'D, gfow/:
cbB ejkT[Adk j?.

9H nphie cbB (Transcendental Function)^
nphie cbB fBwB gqeko d/ j[zd/ jB^
(i) sfoe'Dfwsh cbB (Trigonometrical Functions)^fit/AL sin x, cos x, sec x, sin 2x +
2
sec x nkfd.
–1
–1
–1
–1
(ii) ftgohs r'b cbB (Inverse Circular Functions)^fit/AL sin x, cos x, tan x, sec
x nkfd.
2
(iii) bx[rDeh cbB (Logarithmic Functions)^fit/AL log e x, log a x, log e (x + 4x + 3)
nkfd.

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