Úlohy - limita - jednoduché úlohy
Úloha
\(\lim_{x \to -1} (2x + 3) =\)
- \(= 2(-1) + 3 = \)
- \(= 1\)
Úloha
\(\lim_{x \to 0} (x^2 - 2x + 3) =\)
- \(= 0^2 - 2\cdot0 + 3 = \)
- \(= 3\)
Úloha
\(\lim_{x \to 1} \frac {2x + 3}{3x - 2} =\)
- \(= \frac {\lim_{x \to 1} (2x + 3)}{\lim_{x \to 1}(3x - 2)} = \)
- \(= \frac{2 \cdot 1 + 3}{3 \cdot 1 - 2} = \)
- \(= 5\)
Úloha
\(\lim_{x \to -2} \frac {x^2 - 4}{x - 2} =\)
- \(= \frac {\lim_{x \to -2} (x^2 - 4)}{\lim_{x \to -2}(x - 2)} = \)
- \(= \frac {(-2)^2 - 4}{-2 -2} = \)
- \(= 0\)
Úloha
\(\lim_{x \to 2} \frac {x^2 - 4}{x - 2} =\)
- \(= \lim_{x \to 2} \frac {(x - 2)(x + 2)}{(x - 2)} = \)
- \(= \lim_{x \to 2} (x + 2) = \)
- \(= 4\)
Úloha
\(\lim_{x \to 1} \frac {x^3 - 1}{x - 1} =\)
- \(= \lim_{x \to 1} \frac {(x - 1)(x^2 + x + 1)}{(x - 1)} = \)
- \(= \lim_{x \to 1} (x^2 + x + 1) = \)
- \(= 3\)
Úloha
\(\lim_{x \to -3} \frac {x^2 + 5x + 6}{x^2 + 4x + 3} =\)
- \(= \lim_{x \to -3} \frac {(x + 2)(x + 3)}{(x + 1)(x + 3)} = \)
- \(= \lim_{x \to -3} \frac {x + 2}{x + 1} = \)
- \(= \frac {1}{2}\)
Úloha
\(\lim_{x \to -1} \frac {x^3 + x^2 + x + 1}{x^2 - 2x - 3} =\)
- \(= \lim_{x \to -1} \frac {(x + 1)(x^2 + 1)}{(x + 1)(x - 3)} = \)
- \(= \lim_{x \to -1} \frac {x^2 + 1}{x - 3} = \)
- \(= - \frac {1} {2}\)
Úloha
\(\lim_{x \to -1} \frac {x^3 - x^2 - 1}{x^5 - 2x - 1} =\)
- \(= \lim_{x \to -1} \frac {(x + 1)(x^2 - x - 1)}{(x + 1)(x^4 - x^3 + x^2 - x - 1)} = \)
- \(= \lim_{x \to -1} \frac {x^2 - x - 1}{x^4 - x^3 + x^2 - x - 1} = \)
- \(= \frac {1} {3}\)
