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MATH 211 Test 1 Sample

MATH 211 Test 1 Sample - n(x 4 n(b x n(c(2x 5 2n(d n 2(x...

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MATH 211 Test 1 Sample Problems 1. Compute the limit or explain why it DNE. (a) = (b) = (c) = 2. Find the sum of the series or explain why it diverges. (a) (b) 3. Use geometric series to write each repeating decimal as a fraction of integers. (a) 10.433433433 .... (b) – 0.0012012012 .... 4. Determine whether the series converges or diverges. Be sure to give reasons for your answers. (a) (b) (c) 5. Find the center, a, and the radius of convergence, R. (a) n 2
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Unformatted text preview: n (x + 4) n (b) x n (c) (2x + 5) 2n (d) n 2 (x – 3) n (e) 6. Find a power series for the function at the given center, and give its radius of convergence. (a) ln x = dx, a = 3 (b) , a = 0 (c) , a = 1 7. (a) Use the partial sum S 5 from the series in 6(a) to estimate ln 2. How good is the estimate? (b) Use the series in 6(a) to calculate ln x dx as a series. 8. Use Newton's Method to solve 1 – x 3 = sin x accurate to three decimal places....
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