[r]
(1)C¸c c«ng thøc hµm sè mò – logarit cÇn nhí I - c«ng thøc cña hµm sè mò m n am n =am −n a n n a a = n b b m +n a a =a n ( am ) =am n () ( a b )n =an bn n n n a √a m m n n m n n = n √a m=( √a ) =am n √√ a= √ a b √b 10 a m >an ⇔ m>n : a>1 ; m<n : <a<1 n n ⃗ 11 a<b , a , b : le ❑ a <b II- C«ng thøc hµm sè logarit α α=log a b ⇔ a =b DK:b >0 , 0<a ≠ log a 1=0 ; log a a=1 log a ( b c )=log a b+log a c log a ab=b ; alog b=b log c b lg b ln b b log a =log a b − log a c log a b= = = c log c a lg a ln a 1 log a b= log a b= log a b log b a α log a b> log a c ⇔ b> c : : a>1; b<c: khi: 0< a<1 III- §¹o hµm cña hµm sè : √ n a () α x⃗ x y=a ❑ y ' =a ln a y =log a x ⃗ ❑ y '= x ln a IV- Giíi h¹n cña hµm sè: x x y=e ⃗ ❑ y '=e ⃗ y '= y=ln x ❑ x x =e x x→ ∞ a x −1 lim =ln a x x →0 ( ) lim 1+ ( 1+x )a lim =a x x →0 n √a b=√ a √ b lim ( 1+ x ) x =e x→ ∞ log ( 1+ x ) =log a e x x →0 lim (2)