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around 4 minutes: 36-9=27 Multivariable Calculus: Find all local maxima/minima and saddle points for the function f(x,y) = x^3 + 3xy + y^3. 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Algebra: Here are a few problems on linear maps. Part 1: Are the following maps L:R^3 to R^3 linear? (a) L(x, y, z) = (x+1, x-y-2, y-z), (b) L(x, y, z) = (x + 2y, x-y-2z, 0). Part 2...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/788919/d6d765ed2c1cc94885b60935e7408d77/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/75RXEQEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"8","reqid":"1769514605907655-16945385853644336468-balancer-l7leveler-kubr-yp-klg-216-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DhYvfqpEEYaY","linkTemplate":"/video/preview/8826510666392766275?parent-reqid=1769514605907655-16945385853644336468-balancer-l7leveler-kubr-yp-klg-216-BAL&text=MathDoctorBob&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Examples of Linear Maps","related_orig_text":"MathDoctorBob","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"MathDoctorBob\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=hYvfqpEEYaY\",\"src\":\"serp\",\"rvb\":\"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_4N_gIA-wMDDgoI-wIIAQf69___AOYDBP0J_QEA-fX4-_gAAAAFDfQKBQAAAPf9_vX6_wAACQf7-QQAAAAE__0CAgAAAAEJBQT-AQAA9voG-QIAAAAIBAIKAAAAAP_6ChAAAAAA7AT99QAAAAD28wP9AAAAACAALY2P2js4E0AJSE5QAiqEAhAAGvABf-4AAKb8Kvw68wgA6Nf8Aa33JP8qKQsAs_sZAe7-3gDHBhkA2ejlAfUP8AHg_BsA9dPvAOnSIwAKC-r_Sfce_xEHBgE88uQAIu0QAeX02AAi-g8A3v8RACTlBv8h-_77FQAS_98BAP0sCtwCL_AdAiEQNADU9gD8ANgIBc8SGgE1_usDI_T0BfkC9P3N_hwBAt_1AskOCvkD8h8H7Qf5BP375gIa_878DQbzBisZBgAN-vz5yefm_wgYDwQD_e77CuoWAgAJGQEpDgEADunzBREG7fz48hL5CffgAdzQ9vjn-QEICfQA9tL87gv38g4SIAAtGCAkOzgTQAlIYVACKnMQABpgNAMANdxH3BwiRPbc5xoN8_n_1gvgH_8IwP__-dwlEQ2vwtoF_xfP_cegAAAAC-TazA4AAn_Sx74yPM_4ysPm8ul2yUEM_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_AADgQAAAikIAABBBAABwwQAAYEEAAHhCAACiwgAAoEAAAAAAAADgwAAAGEIAAFDBAABQQQAAiEEAAODAAAAgQQAAWEIAAGzCAAC0wgAAQMEAACzCAAAMQgAACMIAADTCAAAcQgAA-MEAAEDBAADgQAAAUEEAAKBAAACAvwAAAMEAAJhBAACAwQAAQEAAAABAAABAwSAAOBNACUh1UAEqjwIQABqAAgAAVL4AAES-AAC4vQAAuj4AACQ-AACYvQAAFD4AAP6-AAA8vgAAiL0AAHS-AAAEvgAAuL0AAK4-AACOvgAAML0AAMo-AACIPQAAHD4AALY-AAB_PwAA2L0AAJg9AACYPQAAcL0AAHC9AABkPgAAZL4AAAw-AADoPQAAlj4AAKC8AACYvQAAdL4AAIA7AABwvQAABD4AAIa-AADevgAAgr4AAEw-AABkvgAA4DwAAPi9AADYvQAA4DwAAL4-AABsvgAATL4AABy-AAAQPQAAvr4AADQ-AAA8vgAAZD4AAFA9AABXPwAAML0AAEA8AAAUPgAAVL4AADw-AAD4vQAAJL4gADgTQAlIfFABKo8CEAEagAIAALq-AAC4PQAAuL0AADe_AACovQAAZL4AAMo-AABkvgAA0j4AALg9AAAcvgAA-L0AAIA7AACIvQAA2L0AABC9AABkvgAAFT8AAPi9AACuPgAA2D0AAEy-AACgvAAA6D0AAOA8AACgPAAAiL0AAGw-AABsPgAA6L0AABC9AABcPgAANL4AAOi9AABAvAAAHL4AAEc_AABEvgAAdL4AAKg9AAAMPgAAqL0AADS-AACYPQAAND4AALi9AAB_vwAAJD4AANi9AAA8PgAAmL0AAKC8AAA8vgAAJD4AAKg9AABsPgAAqL0AAKi9AAD4PQAA-D0AAEw-AACGvgAAcL0AAMg9IAA4E0AJSHxQATAJOAFKAGAAaAA,\"}","related_url":"http://www.youtube.com/watch?v=hYvfqpEEYaY","parent-reqid":"1769514605907655-16945385853644336468-balancer-l7leveler-kubr-yp-klg-216-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1280,"cheight":720,"cratio":1.77777,"dups":["8826510666392766275"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":true,"contentTypeId":null,"censored":false,"videoContentId":"2828105407"},"1093765735975956362":{"videoId":"1093765735975956362","docid":"34-1-8-Z50A8DAA4E002D09F","description":"Linear Algebra: Given an orthonormal basis of R^n, we present a quick method for finding coefficients of linear combination in terms of the basis. 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We derive the Maclaurin series of f(x) = sqrt(1+x) and use it to compute the series for 1/sqrt(1+x). With this, we obtain the series for sin^{-1}(x), and, in turn, calculate an estimate...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3111959/907f188fc4fff088b4ea1d17dbdbad11/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/gEK1DQEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"15","reqid":"1769514605907655-16945385853644336468-balancer-l7leveler-kubr-yp-klg-216-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D-xIy-9g-Nwg","linkTemplate":"/video/preview/8646547573546069534?parent-reqid=1769514605907655-16945385853644336468-balancer-l7leveler-kubr-yp-klg-216-BAL&text=MathDoctorBob&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"The Maclaurin Series of f(x) = (1+x)^{1/2} 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Find the cube roots of -8 in the complex numbers, and sketch as points in the complex plane. We employ two approaches: one using deMoivre's Theorem, and the other by factoring z^3...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3368406/5ccbfcd1a7a95ebb3c241fc70fc18365/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/XNcDMwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"16","reqid":"1769514605907655-16945385853644336468-balancer-l7leveler-kubr-yp-klg-216-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DYvOtRhjg_rY","linkTemplate":"/video/preview/15444209960795339616?parent-reqid=1769514605907655-16945385853644336468-balancer-l7leveler-kubr-yp-klg-216-BAL&text=MathDoctorBob&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Cube Roots of 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