CALCULUS 1 WORKSHEET #104 REVIEW CALCULATOR _______________________________________________________________________________
The graph of f ’ shown is for Questions 1 and 2 1. f has a local minimum at x = (A) 0 only (B) 4only (C) 0 and 4
(D) 0 and 5
(E) 0,4, and 5
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2. f has a point of inflection at x= (A) 2 only (B) 3 only (C) 4 only (D) 2 and 3 only (E) 2,3, and 4 __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
3. If c is the value defined by the Mean Value Theorem, then for f ( x ) = e x − x 2 on [0,1], c = (A) − 0.248
(B) 0.351
(C) 0.500
(D) 0.693
(E) 0.718
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4. Find the volume of the solid generated when the region bounded by the y-axis, y = e x , and y =2 is rotated around the y-axis: y
x
(A) 0.296
(B) 0.592
(C) 2.427
(D) 3.998
(E) 27.577
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5. If y is a differentiable function of x, then the slope of the curve of xy 2 − 2 y + 4 y 3 = 6 at the point where y = 1 is:
−1 −1 5 −11 (B) (C) (D) (E) 2 18 26 18 18 __________________________________________________________________________________________ (A)
CALCULUS 1 WORKSHEET #104 REVIEW CALCULATOR _______________________________________________________________________________ 6. The acceleration of a particle moving along a straight line is given by a = 6t. If, when t = 0, its velocity, v, is 1 and its position, s, is 3, then at any time t: A) s = t 3 + 3 B) s = t 3 + 3t + 1 C) s = t 3 + t + 3 t3 D) s = + t + 3 3 t3 t2 E) s = + + 3 3 2 ________________________________________________________________________________________ dy is equal to: 7. if y = f ( x 2 ) and f '( x ) = 5x − 1 , then dx
(A) 2 x 5x 2 − 1 (B) 5x − 1 (C) 2 x 5x − 1 5x − 1 (D) 2x (E) none of these _____________________________________________________________________________________ 8. If the area under y = sin x is equal to the area under y = x 2 between x = 0 and x = k, then k= y
x
(A) − 1.105 (B) 0.877 (C) 1.105 (D) 1.300 (E) 1.571 __________________________________________________________________________________________ 9. sin( x 2 )dx =
z
(A) − cos( x 2 ) + C (B) cos( x 2 ) + C − cos( x 2 ) +C 2x (D) 2 x cos( x 2 ) + C (E) none of these __________________________________________________________________________________________ 10. At noon, an experimenter has 50 grams of a radioactive isotope. At noon nine days later only 45 grams remain. To the nearest day, how many days after the experiment started will there be only 20 grams? (A) 54 (B) 59 (C) 60 (D) 75 (E) 78
(C)
CALCULUS 1 WORKSHEET #104 REVIEW CALCULATOR _______________________________________________________________________________ 11. A 26-ft ladder leans against a building so that its foot moves away from the building at the rate of 3ft/sec. When the foot of the ladder is 10 ft from the building, the top is moving down at the rate of r ft/sec, where r is 46 (A) 3 3 (B) 4 5 (C) 4 5 (D) 2 4 (E) 5 __________________________________________________________________________________________ 2x 1 dt , then F’(x) = 12. If F(x) = ∫ 3 1 − t 1 1 1 2 1 2 (A) (B) (C) (D) (E) 3 3 3 3 1− x 1− 2x 1− 2x 1 − 8x 1 − 8x 3 __________________________________________________________________________________________
13. The graph shows an object’s acceleration (in ft/ sec 2 ). It consists of a quarter circle and two line segments. If the object was at rest at t = 5 sec, what was its initial velocity? (A) − 2 ft/sec (B) 3 − π ft/sec (C) 0 ft/sec (D) π − 3 ft/sec (E) π +3 ft/sec __________________________________________________________________________________________ t 14. Water is leaking from a tank at the rate of R(t ) = 5 arctan gallons per hour, where t is the number of 5 hours since the leak began. How many gallons will leak out during the first day. (A) 7 (B) 82 (C) 124 (D) 141 (E)164 __________________________________________________________________________________________
FG IJ HK
CALCULUS 1 WORKSHEET #104 REVIEW CALCULATOR _______________________________________________________________________________ 2 15. Fine the y-intercept of the line tangent to y = x 3 − 4 x 2 + 8 e cos x at x = 2
c
h
(A) − 21.032 (B) − 2.081 (C) 0 (D) 4.161 (E) 21.746 __________________________________________________________________________________________ 1)D 2)D 3)B 4)B 5)A 6)C 7)A 8)D 9)E 10)E 11)C 12)E 13)D 14)C 15)D
