MAT21B-Schultens-Fall-2011

# MAT21B-Schultens-Fall-2011 - 4 Rectangles = 8 Rectangles =...

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Deepti Singh MAT21B-Schultens-Fall-2011 Assignment hw1 due 10/01/2011 at 11:59pm PDT 1. Find an antiderivative P of p ( t ) = 1 3 t 2 . P ( t ) = Answer(s) submitted: 3 t ˆ (1/3) (correct) 2. Find an antiderivative P of p ( s ) = 7sin ( 7 s ) . P ( s ) = Answer(s) submitted: -cos (7s) (correct) 3. Find an antiderivative F of f ( x ) = 8 x 2 + 5 x - 3 . F ( x ) = Answer(s) submitted: 8/3 x ˆ3 + 5/2xˆ2 -3x (correct) 4. Find an antiderivative F of f ( x ) = 6 x 4 - 6 x x 3 . F ( x ) = Answer(s) submitted: 3xˆ2 + 6xˆ-1 (correct) 5. Find an antiderivative H of h ( u ) = 5 e u + 4sec 2 u . H ( u ) = Answer(s) submitted: 6eˆu + 4tanu (incorrect) 6. Estimate the area under the graph of f ( x ) = x sin ( x ) from x = 0 to x = π / 2 by computing lower and upper sums, using the partition { 0 , π / 6 , π / 4 , π / 3 , π / 2 } . Lower Sum = Upper Sum = Answer(s) submitted: 0.688783 1.60824 (score 0.5) 7. (a) Estimate the area under the graph of f ( x ) = 2 x 3 + 3 from x = - 1 to x = 3, first using an upper sum with 4 rectangles, and then improving your estimate using 8 rectangles. 4 Rectangles = 8 Rectangles = (b) Repeat part (a) using lower sums. 4 Rectangles = 8 Rectangles = (c) Repeat part (a) using the midpoint method.

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Unformatted text preview: 4 Rectangles = 8 Rectangles = Answer(s) submitted: • 28 • 39 • 84 • 67 • • (incorrect) 1 8. Estimate the area under the graph of f ( x ) = 2 x + 1 from x = 1 to x = 5 (a) using a lower sum with 4 rectangles; (b) using an upper sum with 4 rectangles. Answer(s) submitted: • 6.566 • 8.166 (correct) 9. Evaluate the sum: 3 ∑ k = ((-1 ) k ( k + 1 ) 2-2 ) . Answer(s) submitted: •-18 (correct) 10. Evaluate the sum: 5 ∑ n = 1 ± 60 7 n ² . Answer(s) submitted: • 9.99 (correct) 11. Find a function f ( k ) such that 5 + 7 + 9 + 11 + 13 = 4 ∑ k = f ( k ) . f ( k ) = Answer(s) submitted: • 2k + 5 (correct) 12. Find the limit of the ﬁnite sums: lim m → ∞ m ∑ n = 1 ± sin ± 1 n ²-sin ± 1 n + 1 ²² . Answer(s) submitted: • sin( 1 ) (correct) Generated by c ± WeBWorK, http://webwork.maa.org, Mathematical Association of America 2...
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