1190 câu hỏi phân loại chuyên đề hàm số mũ

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TUYỂN TẬP 1190 CÂU HỎI

PHÂN LOẠI THEO TỪNG MỨC ĐỘ

(Trích từ gần 200 đề thi thử trên cả nước năm 2017)

CHUYÊN ĐỀ HÀM SỐ LŨY THỪA

HÀM SỐ MŨ HÀM SỐ LÔGARIT

HUẾ - 8/2017

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Câu 336: [THPT An Lão lần 2] Tìm tập xác định D của hàm số   2

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x y Hàm số luôn có một tiệm cận ngang là đường thẳng y 1

Đồ thị hàm số có 3 tiệm cận khi và chỉ khi phương trình g x x2 2mx m 0 có hai nghiệm phân biệt khác 1

y x  xác định khi và chỉ khi x    1 0 x 1 (do số mũ bằng  4 là nguyên âm)

Suy ra tập xác định của hàm số đã cho là D \ 1  

Câu 340: [THPT NGUYỄN QUANG DIÊU] Tìm tập xác định của hàm số  2  2

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Câu 346: [SỞ GD ĐT HÀ TĨNH] Điều kiện xác định của hàm số   3

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1 3

2x 1 ln 2x 1

C

4 3

2

4 3

số xác định:  x 0 Câu 350: [THPT Thuận Thành 2] Tìm tập xác định D của hàm số

1 3

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số xác định:  x 0 Câu 361: [THPT Trần Phú-HP] Hàm số  2  4

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4 1

4

x y

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f x và f x4( ) là hai hàm số mũ với mũ không nguyên nên có tập xác định là  0;  

Câu 372: [THPT Hoàng Văn Thụ - Khánh Hòa] Hàm số  2  1 5

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4 biến trên từng khoảng xác định, loại B

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C Giá trị nhỏ nhấtcủa hàm số bằng e D Hàm số đạt cực trị tại điểm x 1

Hướng dẫn giải Chọn A

Câu 382: [THPT Chuyen LHP Nam Dinh] Tính đạo hàm của hàm số y 1 cos3x6

A y' 18sin 3x cos3x 15 B y' 18sin 3 1 cos3x x 5

C y' 6sin 3 1 cos3x x 5 D y' 6sin 3 cos3x x 15

Hướng dẫn giải Chọn B

f x và f x4( ) là hai hàm số mũ với mũ không nguyên nên có tập xác định là  0;  

Câu 384: [TTLT ĐH Diệu Hiền] Tập xác định của hàm số  2  4

6

y x  x  là

A D \   2;3  B D \ 0  

C D   ; 2    3;   D D

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2 1 0; 2 2

y  

Vậy giá trị nhỏ nhất của hàm số yx4x2 1 trên đoạn   0; 2 là 1 3

4 2

C. Hàm số nghịch biến khi   0 D. Đồ thị hàm số là đường thẳng khi   1

Hướng dẫn giải Chọn B

Chọn đáp án Tập xác định của hàm số là D  0;   vì tập xác định của hàm số là D  0;   khi  không nguyên

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- Nếu x 0 thì x3     1 1 0 y 2 x2  1 2 Vậy: y 2,   x 1, y   2 x 0

Câu 392: [TTGDTX Cam Ranh - Khánh Hòa] Một chuyển động có phương trình là

'' ''

64

as  f t   t   7

1 64

1 log x 4 x (thoả mãn điều kiện)

Câu 394: [TTLT ĐH Diệu Hiền] Tìm tất cả giá trị thực của tham số m sao cho hàm số x 22

  Nên thỏa yêu cầu bài toán

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4 l

; 1; 2 \ 0

1 1

m

m m

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x

 

2 2

x y

x

 

2 ln 5 2

x y x

t n

2 ln 2 sin

t n

2 ln 2 cos

Phương pháp: + Áp dụng công thức tính đạo hàm:  a x  a xlna

Cách giải: Áp dụng công thức trên ta được đáp án: 2017 ln 2017x

Câu 401: [SỞ GD ĐT HƯNG YÊN] Đạo hàm của hàm số y 10x là:

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Câu 404: [Sở GDĐT Lâm Đồng lần 04] Đạo hàm của hàm số ye2x 1sin2xlà:

A y' 2 e2x 1sin 2x2e2x 1 cos 2x B y' 4 e2x 1cos 2x

C y' 2 e2x 1sin 2x2e2x 1 cos 2x D y' 2 e2x 1cos 2x

Hướng dẫn giải Chọn A

vì y' ( e2x 1)'sin 2x e 2x 1(sin 2 )' 2x  e2x 1sin 2x2e2x 1 cos 2x

Câu 405: [TT Tân Hồng Phong] Tính đạo hàm của hàm số   3 1

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bốn hàm số được liệt kê ở bốn phương án A B C D, , , dưới đây Hỏi hàm số đó là hàm số nào ?

Đồ thị đi qua điểm A  0;1 nên ta loại phương án B C,

Đồ thị của hàm số này đồng biến nên ta chọn D.

Câu 412: [THPT Hoàng Văn Thụ (Hòa Bình)] Hàm số nào sau đây đồng biến trên ?

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Câu 421: [THPT CHUYÊN BẾN TRE] Hàm số   x

f x xe .đạt cực đại tại điểm

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Vậy tập nghiệm của phương trình là S    0;1

Câu 424: [SỞ GD-ĐT ĐỒNG NAI] Tìm tập nghiệm S của bất phương trình: 3

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1 ( ) 2

x y

y e

 ,   8

1 2

 trên đoạn   1;1 

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 , y  0  0 Vậy,

Câu 432: [THPT Nguyễn Văn Cừ] Tính đạo hàm của hàm số y 7x2 x 2