>> For square roots, you can use sqrt() or the exponent (1/2). ( )Tj 0000000208 00000 n 601 690.277 l 27 0 obj 1.23e-5. /T1_0 1 Tf (ln\( \) Another name for the natural log )Tj /T1_3 1 Tf /BitsPerComponent 8 /T1_0 1 Tf ( )Tj (m)Tj 14 0 0 14 90 337.6679 Tm /T1_3 1 Tf Non-homogeneous Equation; Method of Undetermined Coefficients. /T1_0 1 Tf /T1_0 1 Tf ( )Tj 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 7 0 0 7 75.139 405.0679 Tm (If a problem calls for a decimal answer, give at least four decimal digi\ ts, or as many as the )Tj information about the form of the answer that is expected. << 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 T* 0 Tc 0 Tw 0 Ts 100 Tz 0 Tr 9 0 0 9 18 780.17 Tm /Name/Im2 stream /ProcSet[/PDF/ImageC] (m)Tj Re ($c) or $c->Re. 0000000016 00000 n C2 = 7 812.5 875 562.5 1018.5 1143.5 875 312.5 562.5] /BBox[0 0 2384 3370] Finally, solve for C2. For )Tj Exponents are taken right to left: 2^3^4 = 2^(3^4) = 2^81 = a big number. endobj /Subtype/Type1 /Filter/FlateDecode ( )Tj /T1_0 1 Tf /Height 24 (latter form, without a space, only provided no misunderstanding is possi\ ble. 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 ( )Tj 500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 777.8 444.4 444.4 ET /Artifact <>BDC (2.1E2 gives 210 )Tj (Other intervals: )Tj example. 0000014929 00000 n /T1_0 1 Tf For example, )Tj /Article <>BDC /DecodeParms<< Step 2. How do I enter square roots or cube roots? T* 14 0 0 14 90 577.0679 Tm If you still have any questions and concerns then please contact me at Rana.Das@mail.citytech.cuny.edu, Tagged undetermined coefficients, videos, webwork. ( )Tj >> -4.107 -2.557 Td (\(4*x\)\)^2 much clearer than 2+3sin\(4x\)^2? 2x, 2 x or 2*x, also 2\(3+\ 4\). CAUTION: (very important) In step 3, before writing homogeneous part of the solution, we have to consider some of the important facts. (http://texas.math.ttu.edu/~gilliam/s06/m1351/howto_enter_answers.html \(\ 1 of 3\)5/1/2009 12:32:45 PM)Tj /T1_3 1 Tf )Tj 9 = C1 + C2 – 7 (5. It's negative. 14 0 0 14 90 160.6679 Tm (then \(sin\(4*x\)\)], next all exponents are taken, giving \(sin\(4*x\)\)\ ^2, next all multiplications )Tj /BaseFont/VIMNIL+CMTT12 0000000371 00000 n /Type/Font /Colors 3 (m)Tj )Tj You should enter: 2+3*\(sin\(4*x\)\ \)^2. (next all multiplications and divisions are performed, giving 3sin\(4x\)^\ 2. 7 0 0 7 75.139 186.6679 Tm answer to be within 2% of the correct value. 14 0 0 14 90 321.0679 Tm (m)Tj 0000015469 00000 n 593.8 500 562.5 1125 562.5 562.5 562.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Your username for WeBWorK consists of your first initial plus your last name, all lowercase (for example, John Smith would have username ‘jsmith’). ( )Tj MATH 10280 WeBWorK Semester 1 2012 Advice on submitting answers If a given answer is not an integer (e.g. T* (universal rules as to which should be done first in the absence of paret\ heses. /DecodeParms<< 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 /T1_0 1 Tf 7 0 0 7 75.139 737.4679 Tm >> Why does the )Tj (1 pt) Evaluate the expression −7−i 5+9i and (m)Tj You w\ rite \(sin\(t\)\)^2 for )Tj /T1_0 1 Tf /T1_0 1 Tf /T1_1 1 Tf 7 0 0 7 75.139 196.6679 Tm /T1_1 1 Tf EMC After appropriate guessing, now, we can process to solve the Non-homogeneous part of differential equation. 14 0 0 14 90 285.0679 Tm Here’s an example. 7 0 0 7 75.139 153.0679 Tm (Cube roots and such)Tj (multiplication. endobj /FontDescriptor 8 0 R The kind of answer that is expected (2,3] U[4,5) is the set . endobj 0000001666 00000 n 21 0 obj /T1_0 1 Tf 0000015054 00000 n First input your values for X, Y, and Z. ( )Tj T* T* 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 514.6 /Colors 3 2009-05-01T12:32:45-04:00 ( )Tj Y (t) = C1e3t + C2 et -7e7t 0000001573 00000 n WolframAlpha, ridiculously powerful online calculator (but it doesn't do everything...) ( )Tj (-infinity,5) is the set . ( )Tj 0 0 0 rg Password. 7 0 0 7 75.139 371.4679 Tm /LastChar 196 You can use them to create complex numbers such as 2i+5.You can also determine the real and imaginary parts of complex numbers and compute other common values such as phase and angle. /Widths[295.1 531.3 885.4 531.3 885.4 826.4 295.1 413.2 413.2 531.3 826.4 295.1 354.2 /T1_1 1 Tf arg ($c) or $c->arg. /Predictor 15 ( )Tj 7 0 0 7 75.139 220.2679 Tm (n)Tj C1 = 9. The question might also require you to enter units or to specify the correct number of significant figures. Algebra. endobj (m)Tj Mathematical Constants Available In WeBWorK . /T1_0 1 Tf 0 i 0000000960 00000 n The (Be careful entering powers of trigonometric, and other, functions. 14 0 0 14 90 337.8679 Tm To get started, you must complete the following three steps. (sinh\( \) )Tj ( )Tj The question might also require you to enter units or to specify the correct number of significant figures. WeBWorK is accessible from on and off campus, anywhere you have access to the internet. The best way to enter this in WeBWorK is by using interval notation: [0,infinity). Im ($c) or $c->Im. To do this, select “Password/Email” from the main menu on the left. BT ( )Tj /T1_0 1 Tf T* Homogeneous equation is a differential equation, which is equal to zero. (exp\( \) The same function as e^x )Tj (m)Tj 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. Prof. Reitz, Tagged help, undetermined coefficients, webwork. /T1_1 1 Tf 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 (sech\( \) )Tj ( )Tj stream /T1_0 1 Tf %%EOF. 761.6 679.6 652.8 734 707.2 761.6 707.2 761.6 0 0 707.2 571.2 544 544 816 816 272 (and divisions are performed, giving 3*\(sin\(4*x\)\)^2. 9 0 0 9 18 7.17 Tm 22 0 obj E.g. 0.875 0.875 0.875 rg 0000015300 00000 n /T1_1 1 Tf x���� ���� ���8��&"�~q�y��G�)��r���������5��k'��S�sN�P$~xʝ�GR"���Y"I�{9T��M�)N�p>��Fo��[�.�Mqh�&>"�M�/�r��|��Y(�Nw���o���o�� O� N[1�Vԗ�8�@q���P���b��b��Pl÷�:��"�� �6�EG�l�Plceq�ج\�(6xa-�e+�ئ��/��Pl3��A�= �m�}��o������@�t�x:b-�=Ue��J��L��(��f���e�v-R޸�++�|J"�U�$���'��x����;�MqkD�5��_�� T* 0000000581 00000 n 602 689.277 l -4.107 -2.557 Td <]>> (m)Tj /T1_0 1 Tf �B��*�' (m)Tj /T1_0 1 Tf i is equivalent to sqrt (-1). /T1_3 1 Tf ( )Tj /Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 0 i f /T1_1 1 Tf (m)Tj (m)Tj Acrobat Web Capture 7.0 Undetermined Coefficients: What happens when everything cancels? 324.7 531.3 590.3 295.1 324.7 560.8 295.1 885.4 590.3 531.3 590.3 560.8 414.1 419.1 (m)Tj The method of undetermined coefficients is a use full technique determining a particular solution to a differential equation with linear constant-Coefficient. (m)Tj )Tj /Subtype/Type1 /T1_1 1 Tf 7 0 0 7 75.139 388.2679 Tm {An example, if r= 7 then Y1 = (e7t)*t}. After we find the roots of the polynomial, the Y, Note: This is homogeneous part of solution. 14 0 0 14 90 119.4679 Tm endstream /T1_1 1 Tf Write each radical as an imaginary number. 7 0 0 7 75.139 321.0679 Tm (3. If you have any trouble – either with logging in, or with completing the assignment, post a comment here or send me an email and I will get back to you. /ProcSet[/PDF/ImageC] (example \(1+2\)*\(3+4\) and \(1+2\)\(3+4\) are both valid. 0 Tc 0 Tw 0 Ts 100 Tz 0 Tr 9 0 0 9 18 780.17 Tm 7 0 0 7 75.139 102.6679 Tm >> endobj 14 0 0 14 130 146.2679 Tm checked. T* to te\ ll the difference )Tj Then write the differential equation expression in tram of C1. BT i��́t�FgFT�°��K;)v��.s�Kmˠs�=�p���Ѐpc�1�#�^���/� �꛷m[�f��u�������Dt���M杢y�H���&���������摱�Y�ٴZMW�e7-�h�T�t1Zg��! 875 531.3 531.3 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 /T1_0 1 Tf ( )Tj -4.107 -2.557 Td 14 0 0 14 90 354.6679 Tm 14 0 0 14 90 232.2679 Tm [���������G���E���"ZD�h-�E���"ZD�h-�E���"ZD�h-�E���"ZD�h-�E���"ZD�h-�E���"ZD����Qo�/lQd}sf��/�� )Tj 0000014711 00000 n cos(pi) is -1, e This gives 2.71828182845905, e.g. Complete the table for each function. /T1_0 1 Tf %PDF-1.2 Click on a problem to see the details (the list of problems appears in the menu on the left). 0000005839 00000 n For example, the square root of two in WeBWorK is either sqrt(2) or 2^(1/2). 11 690.277 l EMC 1 0 0 rg 15 0 obj But sin 2t is really sin\(2\)t, i.e. /T1_0 1 Tf BT ET 0000001242 00000 n Description. /Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 )Tj ( )Tj ( )Tj /T1_0 1 Tf << (34\) but using a * makes things clearer. :�j��e}Q��pq�g�e[6�eeD�q�Y9kzh7x'��%m'�)&��I��(&�-2l���(�|��R�ǠCg"^�o�J�vj��ڏF�W:E��M;�o�g6�@_DS�թދ�}����QpZ4mR��4����,��������'�?��dS�:L�e���6.ӻ)H.�f2-���Խ����8��"��{2���!ܪ���s���u��j���n��|�\���#H��� IU���Dzڲ>M�lڋ��G}:��VO��F��������(���C���E�C����uqX��uL��&ō�B�"���U����qg���⚥��cuWO��3K��9� \#���-K�qYO�6̧ɍ@�j�=�h}�l����%\z���*�^p��%=�gۍ�&gar�|�����ې. 656.3 625 625 937.5 937.5 312.5 343.8 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 14 0 0 14 90 169.8679 Tm 14 0 0 14 90 421.8679 Tm 7 0 0 7 75.139 337.6679 Tm /Subtype/Type1 (m)Tj 545.5 825.4 663.6 972.9 795.8 826.4 722.6 826.4 781.6 590.3 767.4 795.8 795.8 1091 0000015175 00000 n (\(2,3] is the set 2>BDC 24 0 obj New York City College of Technology | City University of New York. -4.107 -2.557 Td Is -5^2 positive or negative? >> (never)Tj that the system would not accept a correct answer). << 14 0 0 14 90 543.8679 Tm \(Indeed, things in parentheses g\ o first, giving \(4x\), )Tj

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