limit as x approaches 0+of 2(1/x-cot(x))

Lösung

x \to 0 + lim (2 (\frac{1}{x} - cot (x)))

0

Schritte zur Lösung

x \to 0 + lim (2 (\frac{1}{x} - cot (x)))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot x \to 0 + lim (\frac{1}{x} - cot (x))

Multipliziere mit der Konjugation von

\frac{1}{x} - cot (x) : \frac{\frac{1}{x ^{2}} - cot ^{2} ( x )}{\frac{1}{x} + cot ( x )}

= 2 \cdot x \to 0 + lim (\frac{\frac{1}{x ^{2}} - cot ^{2} ( x )}{\frac{1}{x} + cot ( x )})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

mit Einschränkung des unbestimmten Ausdrucks

= 2 \cdot \frac{lim _{x \to 0 +} ( \frac{1}{x ^{2}} - cot ^{2} ( x ) )}{lim _{x \to 0 +} ( \frac{1}{x} + cot ( x ) )}

x \to 0 + lim (\frac{1}{x ^{2}} - cot^{2} (x)) = \frac{2}{3}

x \to 0 + lim (\frac{1}{x} + cot (x)) = \infty

= 2 \cdot \frac{\frac{2}{3}}{\infty}

Vereinfache

2 \cdot \frac{\frac{2}{3}}{\infty} : 0

= 0

x \to 2 - lim (\frac{x ^{2} - 1}{x - 2})

x \to 3 lim (- 4 x)

t \to 1 lim (t)

x \to \frac{π}{4} lim (tan (x) - 1)

x \to - 2 lim (f (x) + 5 g (x))