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:
A.
f ( x) x , g ( x) 2x 3.
A. 0
B.
f ( x) 2x 3, g ( x) x.
11. If
C.
f ( x) 2x , g ( x) x 3.
f ’(1)=27, find h’(1).
D.
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) x3 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 tanglent line to the curve x2-y2 = 3 at (2,1).
x 1 2 x3 lim
B. 1
D. L(x) = x
15. The diameter of a sphere is measured as 80cm with a maximum error of 0.5cm. Use differential to estimate the maximum error in calculating the surface area of the sphere.
A. 502.65
B. 125.66
C. 251.32
D. 453.31
16. Find absolute min value of
F(t) = t2(1-t)3 on [0, 2]
A. -4
B. 0
C. -1.5
D. -2
17. Let f(x) = x4+20x. Find inflection points.
A. (0, 0) B. No
C. (1, 21) D. (-1, -19)
18. Verify that f(x) satisfies the hypotheses of
Rolle’s Theorem, and find all numbers c. f(x) = e
A. π/2
sinx
, [0, π].
B. 0
C. π
D. No
19. Let f(2) = 1 and f ’(x) ≥ 3 for 2 ≤ x ≤ 5. How small can f(5) possibly be?
A. 11 B. 4
C. 10
D. 5
20. Find the minimum of the product of 2 numbers with the property that the first is 1 more than twice the second.
A. -1/8
B. 8
C. -8
D. 1/8
21. Find the shortest distance from the point
(2, 1/2) to the parabol y = x2.
A. 3/4 B. 5/4
C.
3/2
5/2
D.
22. Use Newton method to find x3. x3+x-4=0, given x1 = -1.
A. -1.53
B. 2.4286
C. 2.13
D. 2.55
23. A particle is moving with the accerelation a(t)
= sin t-3cos t. Given that s(0)=0 and v(0) = 0. Find s( ).
A. π-6
