Lesson25_-_The_Fundamental_Theorem_of_Calculus_ws

# Lesson25_-_The_Fundamental_Theorem_of_Calculus_ws - t = 5?...

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Section 5.4 The Fundamental Theorem of Calculus V63.0121, Calculus I Spring 2010 Compute the derivatives of the following functions. 1. g ( x ) = Z x 0 sin t dt 2. g ( x ) = Z 3 x 0 sin t dt 3. g ( x ) = Z 0 2 x sin t dt (Hint: reverse the order of the integral.) 4. g ( x ) = Z 3 x 2 x sin t dt (Hint: use the two previous problems.) 5. g ( x ) = Z sin x 0 p 1 + x 3 dx 1

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Let f be the function whose graph is given below. 1 2 3 4 5 6 7 8 9 1 2 3 4 (1,1) (2,2) (3,3) (5,2) Suppose the the position at time t seconds of a particle moving along a coordinate axis is s ( t ) = Z t 0 f ( x ) dx meters. Use the graph to answer the following questions. 6. What is the particle’s velocity at time
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Unformatted text preview: t = 5? 7. Is the acceleration of the particle at time t = 5 positive or negative? 8. What is the particle’s position at time t = 3? 9. At what time during the ﬁrst 9 seconds does s have its largest value? 10. Approximately when is the acceleration zero? 11. When is the particle moving toward the origin? Away from the origin? 12. On which side (positive or negative) of the origin does the particle lie at time t = 9? 2...
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## This note was uploaded on 07/19/2010 for the course MATHEMATIC V63.0121 taught by Professor Leingang during the Spring '09 term at NYU.

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Lesson25_-_The_Fundamental_Theorem_of_Calculus_ws - t = 5?...

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