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Бодлого 5. (Бодолттой)<br />

2<br />

tg(arcsin( )) a<br />

5<br />

бол<br />

x<br />

lim<br />

xa<br />

2<br />

8x12<br />

2<br />

x 4<br />

хязгаарыг бод.<br />

Бодолт: Урвуу функцийн хамаарлын<br />

tg(arcsin x)<br />

<br />

x<br />

1<br />

x<br />

2<br />

ашиглавал:<br />

2 2 2<br />

<br />

2<br />

tg(arcsin( )) <br />

5<br />

<br />

5<br />

<br />

5<br />

2 a 2<br />

5 2 1<br />

2 4<br />

1 ( ) 1<br />

5 5 5<br />

хязгаарыг f(a)=0; g(a)=0 байгаа тохиолдолд уламжлал ашиглан<br />

боддог аргыг ашиглавал:<br />

2<br />

x 8x 12 2x<br />

8 2 ( 2) 8<br />

lim lim 1<br />

x 4 2x<br />

2 ( 2)<br />

x2 2<br />

x2<br />

болно. Функцийн<br />

'<br />

f ( x) f ( x)<br />

lim lim<br />

x a '<br />

g( x) x a g ( x)<br />

гэж гарна.<br />

гэж<br />

Толгойгоо сэргээгээрэй.

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