Differensial va integral hisob komandalarining hususiyatlari 1-§. O‘rta qiymat haqidagi teoremalar

 t   t  c

Teoremadagi (2) shartga asosan lim f (¹ ) ₌ 0, lim g(¹) ₌ 0 bo‘ladi.

t→+0 t t→+0 t

Ushbu,

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 f 1t =  f 1t  ⋅ xt' = − fx' 1t ⋅ 1 ^,  g1t __t = _ g_1t ___x ⋅ xt' = −g'x _1t _⋅ t1₂ t _{  x  } t_

munosabatlardan ( 0;¹c ) intervalda f_t^' (¹_t ), g_t^' (¹_t ) hosilalarning mavjudligi kelib chiqadi. So‘ngra teoremaning 3) shartiga ko‘ra

lim ft' (1t ) = lim − fx'⋅( t12 ) = lim f' (x)

t→+0 g_t' t t x→+∞ g' (x)

Demak f ^_^1_ va g^_^1_ funksiyalarga 1-teoremani qo‘llash mumkin. Bunda