differensiallanuvchi funksiyaning uzluksizligi

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1576162434.doc () ó ax x a d =+d d 0 lim x y a x d® d = d 0 0 lim'() x y fx x d® d = d 0 '()() y fxx x a d =+d d '()() yfxxxx a d=d+dd 0 lim()0 x x a d® d= . ec tg mc j = 1 (0,0,1) ln dxxaa xa >>¹ 1 (ln)'(0) xx x => 2 1 (,) cos2 dxxkkz x p p ¹+î 2 1 (;) sin dxxkkz x p ¹î 2 1 (11) 1 dxx x - 0); 2. d(ax)=ax(lna dx (a>0,a(1); 3.d(logax)= ;xususan, . 4. d(sinx)=cosxdx; 5. d(cosx=-sinxdx; 6. d(tgx)= ; 7. d(ctgx)=- ; 8. d(arcsinx)= ; 9. d(arccosx)=- ; 10. d(arctgx)= dx; 11. d(arcctgx)=- dx . differensial topish qoidalari. funksiya differensiali ta`rifi va hosila topish qoidalaridan quyidagi tasdiqlarning o`rinli ekanligi kelib chiqadi: a) chekli sondagi differensiallanuvchi funksiyalar yig`indisining differensiali ularning differensiallari yig`indisiga teng. masalan, …

erksiz (oraliq) o`zgaruvchi bo`lganda ham bir xil ko`rinishda bo`ladi: differensial hosila va hosila qaysi o`zgaruvchi bo`yicha olinayotgan bo`lsa o`sha o`zgaruvchi differensiali ko`paytmasiga teng bo`ladi. bu xossa differensial ko`rinishning invariantligi deyiladi. shuni aytib o`tish lozimki, bu xossada faqat differensial formasining saqlanishi haqida gap boradi. agar x erkli o`zgaruvchi bo`lsa, u holda dx=(x; x erksiz o`zgaruvchi bo`lsa, u holda, umuman olganda, dx((x bo`ladi. misol. berilgan. 1) x erkli o`zgaruvchi bo`lganda va 2) x=t5+t2-3 bo`lganda dy ni hisoblang. yechish. 1) (2.2) formulaga ko`ra 2) differensial formasining invariantlik xossasidan foydalansak, bo`lib, ga ega bo`lamiz. yuqorida ta`kidlaganimizdek, x0 nuqtada differensiallanuvchi y=f(x) funksiya uchun (y(f`(x0)dx, ya`ni (y(dy taqribiy tenglik o`rinli. shu taqribiy tenglik matematik analizning nazariy va tatbiqiy masalalarida muhim ahamiyatga ega bo`lib, differensialning mohiyatini belgilaydi. yuqoridagi tenglikda (y=f(x)-f(x0), (x=x-x0 deb olsak, quyidagi tenglikka ega bo`lamiz: f(x)-f(x0) (f`(x0)( x-x0) yoki f(x) ( f(x0)+f`(x0)( x-x0) (4.1) (4.1) formula funksiya qiymatlarini taqribiy hisoblashda keng qo`llaniladi. masalan, f(x)= funksiya …

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1576162434.doc () ó ax x a d =+d d 0 lim x y a x d® d = d 0 0 lim'() x y fx x d® d = d 0 '()() y fxx x a d =+d d '()() yfxxxx a d=d+dd 0 lim()0 x x a d® d= . ec tg mc j = 1 (0,0,1) ln dxxaa xa >>¹ 1 (ln)'(0) xx x => 2 1 (,) cos2 dxxkkz x p p ¹+î 2 1 (;) sin dxxkkz x p ¹î 2 1 (11) 1 dxx x - 0); 2. d(ax)=ax(lna dx (a>0,a(1); 3.d(logax)= ;xususan, . 4. d(sinx)=cosxdx; 5. d(cosx=-sinxdx; 6. d(tgx)= ; 7. d(ctgx)=- ; 8. d(arcsinx)= ; 9. d(arccosx)=- ; 10. d(arctgx)= dx; 11. d(arcctgx)=- …

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