Mac10 Review Chap 1 2 3

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MAC101 - Review Chapter 1+2+3

f ( x)  sin  2  x 2

1. Find the range of
A. [0,1]

B. [1,1]

C. [  ,  ]

9. Find horizontal asymptotes of

3x 2  x  1 x2  x  2

D. [0,  ]

2. Describe how the graph of y = f(x-2)+1 is obtained from graph of y = f(x).
A. 2 left, then 1 up.

Bộ môn Toán, ĐH FPT Hà Nội

B. 2 right, then 1up.

A. x = -1

C. y = -3

D. y = 3

10. Find c so that the function is continuous on R

 x 2  cx  c  1 if  g ( x)   x 1
2 if x  1

C. 2 right, then 1 down. D. 2 left, then 1 down.
3. Let

B. x = 2

f ( g ( x))  2x  3. Then:


f ( x)  x , g ( x)  2x  3.

A. 0


f ( x)  2x  3, g ( x)  x.

11. If


f ( x)  2x , g ( x)  x  3.

f ’(1)=27, find h’(1).


f ( x)  x  3, g ( x)  2x.

x 1

A. 3

4. Find limit
A. -1/4

x 3

B. 4

C. 1/4

D. -4

s = 3t2 -2t+7. Find average velocity over [2, 4].
B. 24

C. -16

A. (i)

(ii) x4-x3+1 (iii) cos x (iv) x4 – x2
B. (iii), (iv)

8. Find limit lim x  3

A. -1

B. ∞

C. (iii)

x( x  2) x3 C. -∞

C. 9/4

D. 0

D. 8/27

B. y = 2x-3

C. y = (1/2)x

D. y = (-1/2)x + 2

13. The base of a triangle is increasing at a rate of
1cm/s while the area is increasing at 2cm2/s. At what rate is the altitude changing when the base is
5cm and the area is 100cm2?
A. -7.2

B. 7.2

C. 40

D. -40

14. Find linear approximation for tan x at a=0.

D. (i), (iv)

A. L(x) = -x+1

B. L(x) = -x

C. L(x) = x+1

C. (1/2)f ’(x) D. f ’(x/2)

7. Which functions are even:
(i) sinx

B. 27/8

D. -24

f ( x  2h)  f ( x )
6. What is lim
h 0 h A. f ’(x) B. 2f ’(x)

D. 2

h( x)  3 f ( x) , where f(1)=8 and

A. y = -2x+5

5. The displacement of a moving particle is

A. 16

C. -1

12. Use implicit differentiation to find equation of…...

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