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2.6-bo'lim: Cheksiz limitlar

1-6 muammolar uchun ko'rsatilgan chegaralarni, agar ular mavjud bo'lsa, baholang.

  1. \(\displaystyle f\left( x \right) = \frac{9}{{{{\left( {x - 3} \right)}^5}}}\) baholash uchun,
    1. \(\mathop {\lim }\limits_{x \to {3^{\, - }}} f\left( x \right)\)
    2. \(\mathop {\lim }\limits_{x \to {3^{\, + }}} f\left( x \right)\)
    3. \(\mathop {\lim }\limits_{x \to 3} f\left( x \right)\)
    Yechim
  2. \(\displaystyle h\left( t \right) = \frac{{2t}}{{6 + t}}\) baholash uchun,
    1. \(\mathop {\lim }\limits_{t \to \, - {6^{\, - }}} h\left( t \right)\)
    2. \(\mathop {\lim }\limits_{t \to \, - {6^{\, + }}} h\left( t \right)\)
    3. \(\mathop {\lim }\limits_{t \to \, - 6} h\left( t \right)\)
    Yechim
  3. \(\displaystyle g\left( z \right) = \frac{{z + 3}}{{{{\left( {z + 1} \right)}^2}}}\) baholash uchun,
    1. \(\mathop {\lim }\limits_{z \to \, - {1^{\, - }}} g\left( z \right)\)
    2. \(\mathop {\lim }\limits_{z \to \, - {1^{\, + }}} g\left( z \right)\)
    3. \(\mathop {\lim }\limits_{z \to \, - 1} g\left( z \right)\)
    Yechim
  4. \(\displaystyle g\left( x \right) = \frac{{x + 7}}{{{x^2} - 4}}\) baholash uchun,
    1. \(\mathop {\lim }\limits_{x \to {2^{\, - }}} g\left( x \right)\)
    2. \(\mathop {\lim }\limits_{x \to {2^{\, + }}} g\left( x \right)\)
    3. \(\mathop {\lim }\limits_{x \to 2} g\left( x \right)\)
    Yechim
  5. \(\displaystyle h\left( x \right) = \ln \left( { - x} \right)\) baholash uchun,
    1. \(\mathop {\lim }\limits_{x \to {0^{\, - }}} h\left( x \right)\)
    2. \(\mathop {\lim }\limits_{x \to {0^{\, + }}} h\left( x \right)\)
    3. \(\mathop {\lim }\limits_{x \to 0} h\left( x \right)\)
    Yechim
  6. \(\displaystyle R\left( y \right) = \tan \left( y \right)\) baholash uchun,
    1. \(\mathop {\lim }\limits_{y \to {{{\textstyle{{3\pi } \over 2}}}^{\, - }}} R\left( y \right)\)
    2. \(\mathop {\lim }\limits_{y \to {{{\textstyle{{3\pi } \over 2}}}^{\, + }}} R\left( y \right)\)
    3. \(\mathop {\lim }\limits_{y \to {\textstyle{{3\pi } \over 2}}} R\left( y \right)\)
    Yechim

7 va 8 masalalar uchun berilgan funksiyaning barcha vertikal asimptotalarini toping.

  1. \(\displaystyle f\left( x \right) = \frac{{7x}}{{{{\left( {10 - 3x} \right)}^4}}}\) Yechim
  2. \(\displaystyle g\left( x \right) = \frac{{ - 8}}{{\left( {x + 5} \right)\left( {x - 9} \right)}}\) Yechim