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# calc1quiz-ans - Math 32.02 2 Summation Notation Here is a...

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Math 32.02 Basic Calculus Concepts Lect 01 The following exercises represent some of the most important concepts from ﬁrst-semester calculus. Students who are beginning Math 32 should already be familiar with these concepts. 1 Functions, Limits, and Derivatives 1. lim x a f ( x ) = f ( a ). 2. 0 3. 13 27 4. 1 5. The derivative of f at x , is deﬁned to be f ± ( x ) = lim h 0 f ( x + h ) - f ( x ) h 6. If G ( x ) = a · f ( x ) + b · g ( x ), then G ± ( x ) = a · f ± ( x ) + b · g ± ( x ) 7. If G ( x ) = g ( f ( x )), then G ± ( x ) = g ± ( f ( x )) · f ± ( x ) 8. If G ( x ) = f ( x ) g ( x ), then G ± ( x ) = f ± ( x ) g ( x ) + f ( x ) g ± ( x ) 9. Find the derivatives of the following functions: 135 x 4 + 21 x 2 + 1 cos(2 x ) · 2 x · ln 2 0 - x 1 - x 2 10. 3 2 V 0 wide by 3 p V 0 / 4 high. 11. On the graph below identify which graph is f , f ± and f ±± . Explain your answer. Going top to bottom along the y -axis we have f ± , f , f ±± . Nicholas Robbins. Compiled: August 30, 2006 Page 1 of 2

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Lect 01 Basic Calculus Concepts
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Unformatted text preview: Math 32.02 2 Summation Notation Here is a quick introduction to the summation ( ∑ ) notation for sums and series. 1. 5 2. 30 3. 55 When dealing with sums, it is very important to keep in mind that an index is merely a label to count the terms . For instance, are these pairs equal or not equal? If they are not equal, what it their diﬀerence? 1. Yes 2. No 3. Yes 4. No 5. Yes For each of the following series, write it in Σ notation. 1. Σ ∞ i =0 2 i 2. Σ ∞ i =0 e-i 3. Σ ∞ i =0 (-1) n 4. Σ ∞ i =1 ln ± i i + 1 ¶ 5. Σ ∞ i =1 (-1) i 2 i-1 Page 2 of 2 Nicholas Robbins. Compiled: August 30, 2006...
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calc1quiz-ans - Math 32.02 2 Summation Notation Here is a...

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