វិញ្ញាសារទី៦

1- គណនា​ I= \displaystyle \lim_{x \to 0} \sqrt[x]{1-2x}.

2-(a) គេអោយ y= ln \dfrac{1-x^{2}}{1+x^{2}}; គណនា d^{2}y.

(b)គេអោយ ​y=acoslnx + bsinlnx; a,b ជាចំនួនថេរ។
បង្ហាញថា x^{2}y''+xy'+y=0.

3-(a)គណនា I= \displaystyle \int \dfrac{dx}{sinx+cosx}.

(b) បង្ហាញថា :\int_{o}^{ \pi } xf(sinx).dx= \dfrac{ \pi }{2} \int_{o}^{ \pi } f(sinx).dx.

4-គេអោយ y=sin^{4}x+cos^{4}x;គណនាy^{(1993)}.

5- គេអោយ Z​ជាអនុគមន័នៃ(x,y) និង​ ដេរីវេ :

z'_{x}=arctg \dfrac{y}{x} ;z''_{xy}= \dfrac{y}{x^{2}+y^{2}}.

គណនា d^{2}z(1,0);​កំនត់អនុគមន៍ Z.

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