Mohammed Yaaseen Gomdah MATH 203 Winter 2016 F WeBWorK assignment number Assignment 9 W14 is due : 03/23/2016 at 03:00am EDT. The (* replace with url for the course home page *) for the course contains the syllabus, grading policy and other information. This le is /conf/snippets/setHeader.pg you can use it as a model for creating les which introduce each problem set. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble guring out your error, you should consult the book, or ask a fellow student, one of the TA's or your professor for help. Don't spend a lot of time guessing - it's not very efcient or effective. Give 4 or 5 signicant digits for (oating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 3 instead of 8, sin(3 pi/2)instead of -1, e (ln(2)) instead of 2, (2 + tan(3)) (4 sin(5)) 6 7/8 instead of 27620.3413, etc. Here's the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professors. interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word \"none\". In the last two, your answer should be a comma separated list of x values or the word \"none\". 1. (1 pt) Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.020000 cm thick to a hemispherical dome with a diameter of 50.000 meters. x2 . Find the open intervals on which x+2 f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima). 1. f is increasing on the intervals 9. (1 pt) Let f (x) = 2. (1 pt) Let y = 5x2 + 7x + 2. Find the differential dy when x = 1 and dx = 0.2 Find the differential dy when x = 1 and dx = 0.4 3. (1 pt) Let y = tan(4x + 3). Find the differential dy when x = 2 and dx = 0.4 Find the differential dy when x = 2 and dx = 0.8 2. 4. (1 pt) Let y = 2x2 . Find the change in y, y when x = 4 and x = 0.3 Find the differential dy when x = 4 and dx = 0.3 5. (1 pt) Let y = 3 x. Find the change in y, y when x = 1 and x = 0.1 Find the differential dy when x = 1 and dx = 0.1 6. (1 pt) The linear approximation at x = 0 to A + Bx where A is: and where B is: 7. (1 pt) The linear approximation at x = 0 to where A is: and where B is: The relative minima of f occur at x = Notes: In the rst two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word \"none\". In the last two, your answer should be a comma separated list of x values or the word \"none\". 2 + 5x is 1 2x 4 4 10. (1 pt) Let f (x) = 4 + 2 . Find the open intervals x x on which f is increasing (decreasing). Then determine the xcoordinates of all relative maxima (minima). 1. f is increasing on the intervals is A + Bx 2. 3. The relative minima of f occur at x = f is decreasing on the intervals The relative maxima of f occur at x = 4. f is decreasing on the intervals The relative maxima of f occur at x = 4. The relative maxima of f occur at x = 4. 8. (1 pt) Let f (x) = 6x3 + 3. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima). 1. f is increasing on the intervals 2. 3. f is decreasing on the intervals 3. The relative minima of f occur at x = Notes: In the rst two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word \"none\". In the last two, your answer should be a comma separated list of x values or the word \"none\". Notes: In the rst two, your answer should either be a single Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 1 Mohammed Yaaseen Gomdah E WeBWorK assignment due : 03/23/2016 at 03:00am EDT. 3. 1. (1 pt) Consider the series n=1 n 7n2 + 2 4. Determine whether the series converges, and if it converges, determine its value. If the sum does not converge, enter DNE . 5. 6. (1 pt) Determine the convergence or divergence of the following series. 2n + 1 n2 n=1 A. convergent B. divergent 2. (1 pt) Compute the value of the following improper integral. If it converges, enter its value. Enter innity if it diverges to , and -innity if it diverges to . Otherwise, enter diverges. 1 ne3n n=1 Value (or DNE ): x8 7 n(ln(4n))6 n=1 n=1 Z 2 ln(x) 7 n ln(4n) 7. (1 pt) Determine whether the series is convergent or divergent. If convergent, nd the sum; if divergent, enter div . dx = Does the series 2 ln(n) n8 converge or diverge? ? n=1 n=1 Answer: 8. (1 pt) Match each of the following with the correct statement. C stands for Convergent, D stands for Divergent. 3. (1 pt) Determine whether the series is convergent or divergent. If convergent, nd the sum; if divergent, enter div . n n+4 n n2 + 17 n=1 Answer: 1. 4. (1 pt) Evaluate Z 7x2 ex 3 2. 1 Answer: 3. Determine whether the following series congerges. 4. 2 n3 7n e n=1 5. Enter C if series is convergent, D if series is divergent: 9. (1 pt) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If either test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA rather than CONV.) 5. (1 pt) Test each of the following series for convergence by the Integral Test. If the Integral Test can be applied to the series, enter CONV if it converges or DIV if it diverges. If the integral test cannot be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the Integral Test cannot be applied to it, then you must enter NA rather than CONV.) 1. (ln(n))5 n=1 n + 8 cos(n) n 2. n=1 6n + 9 n+1 1. (6)n n=1 2. ln(n) n=1 7n 4 n7 49 n=1 4 n(n + 5) n=1 4 + 7n 4 + 9n n=1 1 4 + n4 4 n=1 ln (4n) n n=1 1 3. 6n2 CONV.) n3 + 9 n=1 3n6 n3 + 6 n 4. 8 n2 n=1 6n + 5 2 (n) n cos 5. n2 n=1 (ln(n))5 n=1 n + 4 4n5 n8 + 3 n=1 (1)n n=1 9n 6n8 n6 + 4 n 10 5 n=1 9n n + 5 cos2 (n) n n5 n=1 1. 2. 10. (1 pt) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If at least one test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA rather than 3. 4. 5. Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 2