{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Copy of PHAN3_MULOGA - HBM Ton An Giang Ti liu tham kho n...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Chuyên đ HÀM S LŨY TH A, HÀM S VÀ HÀM S LÔGARÍT HĐBM Toán An Giang- Tài li u tham kh o Ôn t p thi TN H TH NG LÝ THUY T : Hàm s lũy th a : Tính ch t c a lũy th a : ▪ V c s ; khi xét lũy th a ơ ố a α : + : α Î ¥ a α xác đ nh a ¡ . + : α - Î ¢ a α xác đ nh khi a ≠ 0 + \ : α Î ¡ ¢ a α xác đ nh khi a > 0. ▪ Tính ch t: V i a, b > 0; m,n ¡ : ; * m m n m n m n n a a a a a a + - = = . ( ) . n m m n a a = ; ( ) . . m m m a b a b = m m m a a b b æö ÷ ç = ÷ ç ÷ ç è ø . ( 0; , ; 0) m n m n a a a m n n = > > Î ¢ 2 k x xác đ nh khi 0 x ³ ( k ¥ ) 2 1 k x + xác đ nh x ¡ ( k ¥ ) ▪ Đ o hàm ( ) / 1 . ( 0, ) x x x α α α α - = > Î ¡ ; ( ) / 1 / . . ( 0, ) u u u u α α α α - = > Î ¡ ( ) / 1 1 ( , 2, 0 , 0 ) . khi n ch½n khi n lÎ n n n x n n x x n x - = > Î ³ ¹ ¥ ; ( ) / / 1 ( , 2, 0 , 0 ) . khi n ch½n khi n lÎ n n n u u n n u u n u - = > Î ³ ¹ ¥ Hàm s : ▪ Hàm s y = a x ( a > 0, a ≠ 1) có t p xác đ nh là ¡ ; t p giá tr là * + ¡ (t c là a x > 0, x ¡ − chú ý tính ch t này đ đ t đi u ki n c a n ph sau này); liên t c trên ¡ . ▪ Đ o hàm ( ) / ln x x a a a = ( a > 0, a ≠ 1) ▪ Khi a > 1 hàm s y = a x đ ng bi n trên ế ¡ . ▪ Khi 0 < a < 1 hàm s y = a x ngh ch bi n trên ế ¡ . a 0 = 1 2200 a 0 , a 1 = a . Trang 26
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
HĐBM Toán An Giang- Tài li u tham kh o Ôn t p thi TN ▪ Khi a > 1: lim x x a + ¥ ® = + ¥ ; lim 0 x x a - ¥ ® = . ▪ Khi 0 < a < 1: lim 0 x x a + ¥ ® = ; lim x x a - ¥ ® =+ ¥ . ▪ V i a > b > 0 ta có: a x > b x x > 0 a x < b x x < 0 . (V đ th c a hàm s trong hai tr ng h p ườ a > 1 0 1 a < < đ nh các tính ch t ) ◙ Hàm s logarit : Chú ý : Khi xét log a x ph i chú ý đi u ki n 0; 1 0. a a x > > ¹ Trong ph n này Ta gi thi t m i bi u th c đ c xét đ u có nghĩa (có ế ượ th yêu c u h c sinh nêu các đi u ki n đ các bi u th c có nghĩa nh : M u ư khác 0, c s ơ ố a, b th a 0 < a,b ≠ 1, đ i s c a logarit ph i d ng). ươ ▪ Cho 0 < a 1 , x > 0: log a x = y a y = x . ▪ V i 0 < a 1 ta có: log a n a n = ( n > 0 ) ; log m a a m = ( 2200 m ¡ ) ; log a 1 = 0; log 1 a a = . ▪ log a ( x 1 .x 2 ) = log a x 1 + log a x 2 ; 1 2 log a x x = log a x 1 - log a x 2 ( x 1 ; x 2 > 0 ). ▪ log a x α = α .log a x ( x > 0) và 1 log .log a a x x α α = ( x > 0, α ≠ 0). ▪ Đ i c s : ơ ố log log log b a b x x a = hay log a x = log a b .log b x log a b = 1 log b a log .log 1 a b b a = . Hàm s y = log a x xác đ nh và liên t c trên (0 ;+ ∞ ). ▪ Đ o hàm ( ) / 1 log .ln a x x a = Khi a > 1 hàm s y = log a x đ ng bi n ế trên ( 0 ; + ∞ ). Khi 0 < a < 1 hàm s y = log a x ngh ch bi n trên ( 0; + ∞ ). ế N u ế a > 1: lim log ; lim log a a x x x x + ¥ - ¥ ® ® =+ ¥ =- ¥ ▪ N u 0 < ế a < 1: lim log ; lim log a a x x x x + ¥ - ¥ ® ® =- ¥ =+ ¥ .
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern