វិញ្ញាសារទី៣

1- គណនា: \displaystyle I= \lim_{x \to 0} \dfrac{x^{2}sin \dfrac{1}{x}}{sinx}

2-(a)គេអោយ y= \dfrac{1}{x^{2}-3x+2};គណនា y_{(o)}^{(1993)}?

(b) y= \biggl ( \dfrac{x}{1+x} \biggr )^{x} គណនា dy?

3-(a)គណនា \displaystyle I= \int_{1}^{e} \displaystyle \frac{lnx}{x \sqrt{1+lnx}}dx

(b) \displaystyle= \int \dfrac{x^{3}+x^{2}+1}{1+x^{4}}dx

4-គណនា \dfrac{d}{d(x^{2})} \bigl( \dfrac{sinx}{x} \bigr ).

5-គេអោយ Z​ ជាអនុគមន៍របស់ (x,y) កំនត់ដោយ: x^{2}+y^{2}+z^{2}=y.e^{ \dfrac{z}{y}}.
-គណនា dz(0,1) when z=0.
-បង្ហាញថា:(x^{2}-y^{2}-z^{2})z'_{x}+2xy.z'_{y}=2xz.
-បង្ហាញថាសមភាពនៅតែផ្តៀងផ្ទាត់ពេល:x^{2}+y^{2}+z^{2}=yf( \dfrac{z}{y}).
ជាមួយ f​ ជាអនុគមន៍ណាមួយដែលមានដេរីវេមួយដង។

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