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These are the notes of Exam of Analytic Geometry and Calculus which includes Limit Number, Recitation, Circle, Correct Response, Series Converge, Statements, True, Converges, Converges Absolutely etc. Key important points are: Items, Formula, Tan, Compute, Slope, Tangent Line, Linear Approximation, Estimate, Number, Derivative
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MA 165 Exam 2 01 Fall 2011
(8 pts) 1. If F (θ) = sin−^1 (√sin θ), then F ′(θ) =
A. 2 √ 1 −cos sin^ θ θ√sin θ
B. (^) 2 sin θcos√ 1 θ− sin θ
C. (^) 2(1 −− sin^ cos θ)^ θ√sin θ
D. cos
(^2) θ 2 √ 1 − sin θ√sin θ E. (^) 2 sin −θ√^ cos 1 −^ θ sin θ
(8 pts) 2. Find the formula for tan (sin−^1 x) A. √ 1 − x^2 B.
√ 1 − x 2 x C. √ 1 x− x 2 D. √1 + x^2 E. √1 +x x 2
(8 pts) 5. If y = xln^ x, then at x = e the value of dy dx is
A. 1 B. 2 C. 3 D. e E. 0
(8 pts) 6. If we use the linear approximation for f (x) = √^3 x at a = 1000, then the estimate for the number √^3 1001 is A. 10. 1 B. 10 C. 10. 2 D. (^30130)
E. (^3001300)
(8 pts) 7. Which of the following is the derivative of ln(2 cosh x)? A. −2 tanh x B. − coth x C. 2 sinh x D. coth x E. tanh x
(8 pts) 8. Evaluate dy if y = x^3 − 2 x^2 + 1, x = 2 and dx = 0.2. A. 0. 6 B. 0. 8 C. 1. 0 D. 1. 2 E. 1. 4
(8 pts) 11. Water is leaking out of an inverted conical tank at a rate of 10000 cm^3 /min. At the same time water is pumped into the tank at a constant rate of r cm^3 /min. The tank has height 12 m and the diameter of the top is 4 m. If water is rising at a rate of 20 cm/min when the height is 2 m, what is the constant rate r? A. 10000
1 − 36 π
cm^3 /min
B.
−10000 +^200009 π
cm^3 /min
C.
10000 − 8000009 π
cm^3 /min
1 +^209 π
cm^3 /min
E. 10000
1 + 36 π
cm^3 /min
(8 pts) 12. A light house is located on a small island, 4 km from the nearest point P on a straight shoreline, and its light makes 5 rotations per minute (10π rad/min). How fast is the beam of light moving along the shoreline when it is 2 km from P? A. 50 π km/min B. 200 π km/min C. 20 π km/min D. (20√5)π km/min E. (40√5)π km/min