2011 Λύσεις Σχ. β&I

5 h ëùôìâóë âíûˆûë âóè ùë ìôúê

Info icon This preview shows pages 84–86. Sign up to view the full content.

View Full Document Right Arrow Icon
5. H ˙ËÙÔ‡ÌÂÓË Â͛ۈÛË Â›Ó·È Ù˘ ÌÔÚÊ‹˜ C = · Ø F + ‚ ÂÂȉ‹ ÙÔ ÓÂÚfi ·- ÁÒÓÂÈ ÛÙÔ˘˜ 0ÆC ‹ ÛÙÔ˘˜ 32ÆF, ı· ÈÛ¯‡ÂÈ 0 = · Ø 32 + ‚. (1) ∂Âȉ‹, ÂÈϤÔÓ, ÙÔ ÓÂÚfi ‚Ú¿˙ÂÈ ÛÙÔ˘˜ 100ÆC ‹ ÛÙÔ˘˜ 212ÆF, ı· ÈÛ¯‡ÂÈ 100 = · Ø 212 + ‚. (2) ∞Ó ·Ê·ÈÚ¤ÛÔ˘Ì ηٿ ̤ÏË ÙȘ (1) Î·È (2) ‚Ú›ÛÎÔ˘Ì 100 = · Ø 180, ÔfiÙÂ Î·È ÂÔ̤ӈ˜ . ÕÚ·, Ë ˙ËÙÔ‡ÌÂÓË Â͛ۈÛË Â›Ó·È ∞Ó ˘¿Ú¯ÂÈ ıÂÚÌÔÎÚ·Û›· Ô˘ Ó· ÂÎÊÚ¿˙ÂÙ·È Î·È ÛÙȘ ‰‡Ô Îϛ̷Θ Ì ÙÔÓ ·ÚÈıÌfi Δ, ÙfiÙ ı· ÈÛ¯‡ÂÈ Δ = (Δ – 32) 9Δ = 5Δ –5 Ø 32 4Δ = –5 Ø 32 Δ = –40. ÕÚ· ÔÈ –40ÆF ·ÓÙÈÛÙÔÈ¯Ô‡Ó ÛÙÔ˘˜ –40ÆC. 6. ∏ ÁÚ·ÊÈ΋ ·Ú¿ÛÙ·ÛË Ù˘ f ·ÔÙÂÏ›ٷÈ: ∞fi ÙÔ ÙÌ‹Ì· Ù˘ ¢ı›·˜ y = –x + 2 ÙÔ˘ ÔÔ›Ô˘ Ù· ÛËÌ›· ¤¯Ô˘Ó ÙÂÙÌË̤ÓË x (– ∞, 0]. ∞fi ÙÔ ÙÌ‹Ì· Ù˘ ¢ı›·˜ y = 2 ÙÔ˘ ÔÔ›Ô˘ Ù· ÛËÌ›· ¤¯Ô˘Ó ÙÂÙÌË̤ÓË x [ 0, 1] Î·È 5 9 C = 5 9 (F – 32). C = 5 9 F – 5 9 32 ‚ = – 5 9 32 · = 5 9 ∫∂º∞§∞π√ 6: μ∞™π∫∂™ ∂¡¡√π∂™ Δø¡ ™À¡∞ƒΔ∏™∂ø¡ 84
Image of page 84

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
∞fi ÙÔ ÙÌ‹Ì· Ù˘ ¢ı›·˜ y = x + 1 ÙÔ˘ ÔÔ›Ô˘ Ù· ÛËÌ›· ¤¯Ô˘Ó ÙÂÙÌË- ̤ÓË x [1, + ∞). 7. i) OÈ Ú›˙˜ Â͛ۈÛ˘ f(x) = 1 Â›Ó·È ÔÈ ÙÂÙÌË̤Ó˜ ÎÔÈÓÒÓ ÛËÌ›ˆÓ Ù˘ y = f(x) Î·È Ù˘ ¢ı›·˜ y = 1, ‰ËÏ·‰‹ ÔÈ ·ÚÈıÌÔ› –1 Î·È 1. √È Ú›˙˜ Ù˘ Â͛ۈÛË f(x) = x Â›Ó·È ÙÂÙÌË̤Ó˜ ÙˆÓ ÎÔÈÓÒÓ ÛËÌ›ˆÓ Ù˘ y = f(x) Î·È Ù˘ ¢ı›·˜ y = x, ‰ËÏ·‰‹ ÔÈ ·ÚÈıÌÔ› –2, 0 Î·È 1. ii) √È Ï‡ÛÂȘ Ù˘ ·Ó›ÛˆÛ˘ f(x) < 1 Â›Ó·È ÔÈ ÙÂÙÌË̤Ó˜ ÙˆÓ ÛËÌ›ˆÓ Ù˘ y = f(x) Ù· ÔÔ›· ‚Ú›ÛÎÔÓÙ·È Î¿Ùˆ ·fi ÙËÓ Â˘ı›· y = 1, ‰ËÏ·‰‹ ÔÈ ·ÚÈıÌÔ› x (– ∞, 1) – {–1}. √È Ï‡ÛÂȘ Ù˘ ·Ó›ÛˆÛ˘ f(x) ≥ x Â›Ó·È ÔÈ ÙÂÙÌË̤Ó˜ ÙˆÓ ÛËÌ›ˆÓ Ù˘ y = f(x) Ù· ÔÔ›· ‚Ú›ÛÎÔÓÙ·È ¿Óˆ ·fi ÙËÓ Â˘ı›· y = x ‹ ÛÙËÓ Â˘ı›· ·˘Ù‹, ‰ËÏ·‰‹ Ù· ÛËÌ›· x [– 2, 0] [1, + ∞). 8. i) √È ÁÚ·ÊÈΤ˜ ·Ú·ÛÙ¿ÛÂȘ ÙˆÓ f(x) = |x| Î·È g(x) = 1 ‰›ÓÔÓÙ·È ÛÙÔ ‰ÈÏ·Ófi Û¯‹Ì·. OÈ Ï‡ÛÂȘ Ù˘ ·Ó›ÛˆÛ˘ |x| ≤ 1 Â›Ó·È ÔÈ ÙÂÙÌË̤Ó˜ ÙˆÓ ÛËÌ›ˆÓ Ù˘ y = |x| Ô˘ ‚Ú›ÛÎÔÓÙ·È Î¿Ùˆ ·fi ÙËÓ Â˘ı›· y = 1 ‹ ÛÙËÓ Â˘ı›· ·˘Ù‹, ‰ËÏ·‰‹ Ù· x [– 1, 1 ].
Image of page 85
Image of page 86
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern