Guia De Ejercicios Segundo Parcial

  • July 2020
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 ǡ ǡ Ǥ  ǡ ǡ Ǥ

ͳǤǦ‡ƒŽ‘•˜‡…–‘”‡•Ǥ

ܽԦ ൌ ൫ʹǡ െͶǡ ξʹ൯ǢܾሬԦ ൌ ሺͲǡʹǡͳሻǢ ܿԦ ൌ ݅ ൅ ͵݇Ǣ݀Ԧ ൌ െ݅ ൅ ͵݆ െ ͸݇

‡–‡”‹‡ǣ

ƒǤǦܽԦ ൅ ܾሬԦ െ ܿԦ„ǤǦ݀ԦǤ ܽԦ ൅ ܾሬԦǤ ܿԦ

…ǤǦܾሬԦሺܽԦ ൅ ݀Ԧሻ†ǤǦܿԦ െ ݀Ԧ ൅ ܽԦ

‡ǤǦܿԦǤ ܽԦ െ ݀ԦǤ ܿԦ

ƒŽŽ‡‡Ž˜‡…–‘”  ƒ…ƒ†ƒ—‘†‡Ž‘•˜‡…–‘”‡•†ƒ†‘‡‡Ž’”‘„Ž‡ƒǤ 

ʹǤǦ‡–‡”‹‡‡Ž’”‘†—…–‘…”—œ’ƒ”ƒ‡Ž’ƒ”†‡Ž‘•˜‡…–‘”‡•†ƒ†‘•ƒ…‘–‹—ƒ…‹×Ǥ ƒǤǦ‫ݑ‬ ሬԦ ൌ െ͵݅ െ ʹ݆ ൅ ݇‫ݒ‬Ԧ ൌ െ݅ ൅ ͹݆ െ ͵݇

„ǤǦ‫ݑ‬ ሬԦ ൌ ʹ݅ െ ͵݆ ൅ ͷ݇‫ݒ‬Ԧ ൌ ͵݅ െ ݆ െ ݇ …ǤǦ‫ݑ‬ ሬԦ ൌ ݆ܽ ൅ ܾ݇‫ݒ‬Ԧ ൌ ܿ݅ ൅ ݀݇

†ǤǦ‫ݑ‬ ሬԦ ൌ ͳͲ݅ ൅ ͹݆ െ ͵݇‫ݒ‬Ԧ ൌ െ͵݅ ൅ Ͷ݆ െ ͵݇ 

͵ǤǦ‡–‡”‹‡†‘•˜‡…–‘”‡•—‹–ƒ”‹‘•‘”–‘‰‘ƒŽ‡•ƒ‫ݑ‬ ሬԦ ൌ ʹ݅ െ ͵݆›‫ݒ‬Ԧ ൌ Ͷ݆ ൅ ͵݇ ͶǤǦ‡–‡”‹‡‡Ž˜ƒŽ‘”†‡Ž•‡‘†‡Žž‰—Ž‘‡–”‡Ž‘•˜‡…–‘”‡•‫ݑ‬ ሬԦ ൌ ʹ݅ ൅ ݆ െ ݇

‫ݒ‬Ԧ ൌ െ͵݅ െ ʹ݆ ൅ Ͷ݇

ͷǤǦƒŽ…—Ž‡‡Ž˜‘Ž—‡‰‡‡”ƒ†‘’‘”Ž‘•˜‡…–‘”‡•‫ݑ‬ ሬԦ ൌ ሺʹǡ െͳǡͲሻ‫ݒ‬Ԧ ൌ ሺͳǡͲǡͶሻ ‫ݓ‬ ሬሬԦ ൌ ሺെͳǡ͵ʹሻ

ʹ •‡ƒ‫ ܣ‬ൌ ൭Ͷ ͳ ‫ݑܣ‬ ሬԦǡ ‫ݒܣ‬ԦǤ ‫ݓܣ‬ ሬሬԦ



͵ ͳ െͳ ͷ൱…ƒŽ…—Ž‡ƒŠ‘”ƒ‡Ž˜‘Ž—‡‰‡‡”ƒ†‘’‘”Ž‘•˜‡…–‘”‡• Ͳ ͸

͸ǤǦ‡ƒ ͸Ǥ

‫ܪ‬ଵ ൌ ሼሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݖ‬ሻ ‫ܴ א‬ଷ ǣ ‫ ݔ‬൅ ‫ ݕ‬െ ‫ ݖ‬ൌ Ͳሽ

‫ܪ‬ଶ ൌ ሼሺ‫ݔ‬ǡ ‫ݕ‬ǡ ‫ݖ‬ሻ ‫ܴ א‬ଷ ǣ ‫ ݔ‬൅ ‫ ݕ‬൅ ‫ ݖ‬ൌ Ͳሽ

ƒǤǦ‡—‡•–”‡“—‡‫ܪ‬ଵ ൅ ‫ܪ‬ଶ ൌ ሼ‫ ݑ‬൅ ‫ݒ‬ǣ‫ܪ א ݑ‬ଵ ‫ܪ א ݒ‬ଶ ሽ‡•—•—„‡•’ƒ…‹‘˜‡…–‘”‹ƒŽ†‡ܴଷ  „ǤǦ ƒŽŽƒ”Žƒ†‹‡•‹×†‡‫ܪ‬ଵ ൅ ‫ܪ‬ଶ  

͹ǤǦ ͹ǤǦ‡–‡”‹ƒ”•‹‡Ž…‘Œ—–‘†‡’‘Ž‹‘‹‘•൛Ȃ ‫ݔ‬ǡ ‫ ݔ‬ଶ െ ʹ‫ݔ‬ǡ ͵‫ ݔ‬൅ ͷ‫ ݔ‬ଶ ൟ‫ܲ׋‬ଶ‡•Ž‹‡ƒŽ‡–‡ ‹†‡’‡†‹‡–‡‘Ž‹‡ƒŽ‡–‡†‡’‡†‹‡–‡Ǥ 

ͺǤǦ ͺǤǦܲଷ †‡…‹†ƒ•‹Ž‘•˜‡…–‘”‡•ሼሺ‫ݐ‬ሻǡ ሺͳ െ ‫ݐ‬ሻǡ ሺʹ‫ ݐ‬ଶ ൅ ‫ ݐ‬െ ͸ሻሽ•‘Ž‹‡ƒŽ‡–‡ ‹†‡’‡†‹‡–‡Ǥ ‫ݔ‬ ͻǤǦ ͻǤǦ‡ƒ‫ ܪ‬ൌ ቊቆ‫ݕ‬ቇ ‫ܴ א‬ଷ ǣʹ‫ ݔ‬െ ‫ ݕ‬൅ ͵‫ ݖ‬ൌ Ͳቋ ‫ݖ‬

ƒǤǦ‡—‡•–”‡“—‡ ‡••—„‡•’ƒ…‹‘†‡ܴଷ  „ǤǦ ƒŽŽ‡—ƒ„ƒ•‡’ƒ”ƒ Ǥ …ǤǦ ƒŽŽ‡†‹‡•‹×†‡ Ǥ

ͳͲǤǦ ͳͲǤǦ‡ƒŽƒ•”‡…–ƒ•†‡‡…—ƒ…‹‘‡•

‫ ݔ‬ൌ ͳ ൅ ͵‫ݐ‬ ‫ݖ‬െͳ  ‫ܮ‬ଵ ൌ ൝ ‫ ݕ‬ൌ ʹ ൅ ‫ܮݕ  ݐ‬ଶ ൌ ሺ‫ ݔ‬െ ͵ሻ ൌ ሺ‫ ݕ‬െ ʹሻ ൌ ͵ ‫ ݖ‬ൌ͵൅‫ݐ‬

ƒŽŽ‡Žƒ‡…—ƒ…‹×†‡Ž’Žƒ‘“—‡…‘–‹‡‡ƒ„ƒ•”‡…–ƒ•ሺ•‹‡š‹•–‡ሻ ͳͳǤǦ ͳͳǤǦ‡ƒܹ ൌ ሼܽ‫ ݔ‬ଷ ൅ ܾ‫ ݔ‬ଶ ൅ ܿ‫ ݔ‬൅ ݀ ‫ܲ א‬ଷ ǣ ܾ െ ݀ ൌ Ͳሽ

ƒǤǦ‡—‡•–”‡“—‡‡•—•—„‡•’ƒ…‹‘˜‡…–‘”‹ƒŽ†‡ܲଷ 

„ǤǦ ƒŽŽ‡—ƒ„ƒ•‡’ƒ”ƒǤ

ଷ ଷ ͳʹǤǦܲ ͳʹǤ ଷ †‡–‡”‹ƒ”•‹‫ݒ‬ଵ ൌ ͳ ൅ ʹ‫ ݐ‬൅ ‫ݒ ݐ‬ଶ ൌ ͳ ൅ ‫ݒݐ‬ଷ ൌ ͳ ൅ Ͷ‫ ݐ‬൅ ͵‫‘ ‘• ݐ‬Ǥ



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